Backscattered Radiation in the Vaidya Metric Near Zero Mass by Waugh and Lake.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 13.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    197466,       5151]
NotebookOptionsPosition[    181904,       4880]
NotebookOutlinePosition[    182392,       4898]
CellTagsIndexPosition[    182349,       4895]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\<\
Notebook for :  
Backscattered Radiation in the Vaidya Metric Near Zero Mass by Waugh and Lake \
\>", "Title",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82084045456205*^9, 3.820840492017107*^9}, 
   3.829146378772785*^9, {3.829160025406114*^9, 3.829160036869446*^9}, {
   3.829208906597193*^9, 3.8292089230442533`*^9}, {3.829239384966258*^9, 
   3.8292393884695873`*^9}, {3.829240028173908*^9, 3.829240035886052*^9}, 
   3.8555050336800833`*^9, 3.855505119277564*^9, {3.8777925053144217`*^9, 
   3.877792516074902*^9}, {3.877793771235619*^9, 3.8777937912119007`*^9}},
 TextAlignment->Center,ExpressionUUID->"5b436d6b-8fd2-4fb6-8187-ad949a029f8c"],

Cell["\<\
Geoff Cope
University of Utah
\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\|01040f\|01042d\|01044c\|010432\|010442\|010432\
\|010449\|010445\|01042e\|01043b\|010428 \|010432\|010442 \|01040f\|01042d\
\|01043b\|01042b
November 18, 2022\
\>", "Author",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.821729507652328*^9, 3.821729529657844*^9}, 
   3.8220480097522783`*^9, {3.822048070235491*^9, 3.822048084689715*^9}, {
   3.8225654346519403`*^9, 3.8225654361641483`*^9}, {3.8231764728567343`*^9, 
   3.823176482313031*^9}, {3.8233640113399878`*^9, 3.823364023347041*^9}, {
   3.8234229506702557`*^9, 3.823422956381791*^9}, {3.827953252419902*^9, 
   3.827953254868108*^9}, {3.851065213363542*^9, 3.8510652255731983`*^9}, {
   3.8510652620952*^9, 3.851065307413348*^9}, {3.851099255534511*^9, 
   3.851099264486588*^9}, {3.851252093025189*^9, 3.851252093273655*^9}, 
   3.851252176997463*^9, 3.8512537234246607`*^9, 3.85125469290289*^9, 
   3.851256927304118*^9, {3.855405234504258*^9, 3.855405238736866*^9}, 
   3.855405272664227*^9, {3.855407872416093*^9, 3.855407879483934*^9}, 
   3.8554963948316936`*^9, {3.855504241007119*^9, 3.855504245254983*^9}, 
   3.8555049671827374`*^9, {3.85550510971922*^9, 3.855505119277684*^9}, {
   3.877792521469215*^9, 3.877792526957705*^9}, 3.877793793915689*^9},
 TextAlignment->Center,ExpressionUUID->"1d2f7d97-d716-4043-9aba-ccc880eadb07"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Hyperlink To Documentation", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.820944675605734*^9, 3.8209446931410646`*^9}, 
   3.829147283859188*^9},ExpressionUUID->"6a3e8038-bd4a-4bea-9bbb-\
de286ad7443f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<GeneralRelativityTensors Documentation and Download\>\"", ",", 
   "\[IndentingNewLine]", 
   "\"\<https://github.com/BlackHolePerturbationToolkit\>\""}], 
  "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.820944619768764*^9, 3.820944681268063*^9}, 
   3.8291472838594027`*^9},
 CellLabel->"In[1]:=",ExpressionUUID->"d70633e0-19e6-42ef-a9f6-330242d88526"],

Cell[BoxData[
 TemplateBox[{
  "\"GeneralRelativityTensors Documentation and Download\"", 
   "https://github.com/BlackHolePerturbationToolkit"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.820944653562152*^9, 3.820944681268403*^9}, 
   3.821729905862431*^9, 3.821732641380642*^9, 3.8218069931429567`*^9, 
   3.821811425912986*^9, 3.822042652654992*^9, {3.822048793766124*^9, 
   3.8220488009116488`*^9}, 3.82250502887521*^9, 3.822505578829629*^9, 
   3.822565490613895*^9, 3.8225662097813597`*^9, 3.822606717894772*^9, 
   3.822739433713368*^9, 3.822822210464344*^9, 3.8233594284652433`*^9, 
   3.8233607803938913`*^9, 3.823360880234103*^9, 3.823361224481102*^9, 
   3.82336209870968*^9, 3.823364030542309*^9, 3.823597528606563*^9, 
   3.823618495251218*^9, 3.82368341365138*^9, 3.82368384184562*^9, 
   3.823684775269041*^9, 3.823688794270237*^9, 3.82369077711421*^9, 
   3.823704572306265*^9, 3.8239670360944*^9, 3.8239675178827963`*^9, 
   3.823970038559888*^9, 3.824025681964837*^9, 3.824032150329472*^9, 
   3.824050435315671*^9, 3.824050999906499*^9, 3.824051492117627*^9, 
   3.824054172450189*^9, 3.824054375215625*^9, 3.829036933263262*^9, 
   3.82914728385952*^9, 3.829160156824955*^9, 3.829239524254714*^9, 
   3.8292401192473373`*^9, 3.87779216062988*^9, 3.877792207882956*^9, 
   3.877792700375227*^9, 3.877794011495726*^9, 3.8777951867764597`*^9},
 CellLabel->"Out[1]=",ExpressionUUID->"df0a06d5-7572-4887-831f-4b2c648166cc"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Hyperlink To Paper", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820840779128604*^9, 3.820840813425404*^9}, {
  3.829147267891533*^9, 3.829147271507358*^9}, {3.8555051221353693`*^9, 
  3.855505123711285*^9}},ExpressionUUID->"976370e4-e7b9-45a6-80f4-\
877ac8b1345e"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Backscattered Radiation in the Vaidya Metric Near Zero Mass by Waugh \
and Lake \>\"", ",", 
   "\"\<https://d1wqtxts1xzle7.cloudfront.net/31929142/0375-9601%2886%2990304-\
x__B._Waugh__Kayll_Lake_--_Backscattered_radiation_in_the_Vaidya_metric_near_\
zero_mass.pdf20130921-9107-n7gvdc-libre-libre.pdf?1379795703=&response-\
content-disposition=inline%3B+filename%3DBackscattered_Radiation_in_the_\
Vaidya_Me.pdf&Expires=1668808427&Signature=BdwxKeZId380kuq~Wjqd6s9eXz~\
Oep8x0p5b0r3pIxXrVm9VEPZZsRjsC-SxmyO8-Ai2d6b36aHFooWtvFiLW74G8g~\
qs558yPAtRdAcNWaVI7nn9lqMb5maxVwagw7s-nxvwAnLTts6slqw~vntvGFr8~TQ3Zo0FgEEa-\
2eSlvIIimz3RmTYe4KgOls7ZtyIiSWhAyTRXE4XGdNftAUZ4r~\
lycXpWwrs5q4Km2BLpQgY9PzIQ5lfdZN6BnTgYE1qV9Uyg3THkOUdrvtcH62ScL5gS7vfsmvXXW3u1\
5EwGM4tQ0Yfkuphwq0Tn2yjVxA-OebzYmibtATNfJ3tSmdIA__&Key-Pair-Id=\
APKAJLOHF5GGSLRBV4ZA\>\""}], "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.877793833373396*^9, 3.8777938584290543`*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"0c810eb3-9ccb-4111-be8c-43d019b37943"],

Cell[BoxData[
 TemplateBox[{
  "\"Backscattered Radiation in the Vaidya Metric Near Zero Mass by Waugh and \
Lake \"", 
   "https://d1wqtxts1xzle7.cloudfront.net/31929142/0375-9601%2886%2990304-x__\
B._Waugh__Kayll_Lake_--_Backscattered_radiation_in_the_Vaidya_metric_near_\
zero_mass.pdf20130921-9107-n7gvdc-libre-libre.pdf?1379795703=&response-\
content-disposition=inline%3B+filename%3DBackscattered_Radiation_in_the_\
Vaidya_Me.pdf&Expires=1668808427&Signature=BdwxKeZId380kuq~Wjqd6s9eXz~\
Oep8x0p5b0r3pIxXrVm9VEPZZsRjsC-SxmyO8-Ai2d6b36aHFooWtvFiLW74G8g~\
qs558yPAtRdAcNWaVI7nn9lqMb5maxVwagw7s-nxvwAnLTts6slqw~vntvGFr8~TQ3Zo0FgEEa-\
2eSlvIIimz3RmTYe4KgOls7ZtyIiSWhAyTRXE4XGdNftAUZ4r~\
lycXpWwrs5q4Km2BLpQgY9PzIQ5lfdZN6BnTgYE1qV9Uyg3THkOUdrvtcH62ScL5gS7vfsmvXXW3u1\
5EwGM4tQ0Yfkuphwq0Tn2yjVxA-OebzYmibtATNfJ3tSmdIA__&Key-Pair-Id=\
APKAJLOHF5GGSLRBV4ZA"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.87779386050043*^9, 3.8777940115328903`*^9, 
  3.877795187247787*^9},
 CellLabel->"Out[2]=",ExpressionUUID->"a795de3b-ddec-462c-8a73-9036f38bedac"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Strengths of singularities in Vaidya spacetirnes by Rajagopal and Lake\
\>\"", ",", "\[IndentingNewLine]", 
   "\"\<https://journals.aps.org/prd/abstract/10.1103/PhysRevD.35.1531\>\""}],
   "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8777925439727*^9, 3.877792555027727*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"8b9e3926-43b0-47f1-8a4c-ff6d88a3b258"],

Cell[BoxData[
 TemplateBox[{
  "\"Strengths of singularities in Vaidya spacetirnes by Rajagopal and \
Lake\"", "https://journals.aps.org/prd/abstract/10.1103/PhysRevD.35.1531"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.877792556469986*^9, 3.8777927004107313`*^9, 
  3.877794011541215*^9, 3.877795187287552*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"38979afc-f31f-4865-a12a-b4467f33cfbf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Naked singularities in self-similar gravitational collapse by Lake & \
Zannias\>\"", ",", "\[IndentingNewLine]", 
   "\"\<https://journals.aps.org/prd/abstract/10.1103/PhysRevD.41.3866\>\""}],
   "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.855505056673311*^9, 3.8555050666159143`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"1b338a7e-8db4-4038-a521-37c84f78e74b"],

Cell[BoxData[
 TemplateBox[{
  "\"Naked singularities in self-similar gravitational collapse by Lake & \
Zannias\"", "https://journals.aps.org/prd/abstract/10.1103/PhysRevD.41.3866"},
  
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.855505068141218*^9, 3.877792160665019*^9, 
  3.877792207919536*^9, 3.877792700419107*^9, 3.877794011560223*^9, 
  3.8777951873025017`*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"30ffb02f-bbe8-4253-98fa-41dba1f8fc99"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Utilities and Package Load", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.820840356577752*^9, 3.820840385449525*^9}, 
   3.829160465380818*^9},ExpressionUUID->"a339e41a-05b8-4914-ba69-\
4e3fb10cf2dd"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}], "\[IndentingNewLine]", 
 RowBox[{"<<", "Utilities`CleanSlate`"}], "\[IndentingNewLine]", 
 RowBox[{"CleanSlate", "[", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ClearInOut", "[", "]"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pdConv", "[", "f_", "]"}], ":=", 
  RowBox[{"TraditionalForm", "[", 
   RowBox[{"f", "/.", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Derivative", "[", "inds__", "]"}], "[", "g_", "]"}], "[", 
      "vars__", "]"}], "\[RuleDelayed]", 
     RowBox[{"Apply", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"Defer", "[", 
         RowBox[{"D", "[", 
          RowBox[{
           RowBox[{"g", "[", "vars", "]"}], ",", "##"}], "]"}], "]"}], "&"}], 
       ",", 
       RowBox[{
        RowBox[{"Transpose", "[", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", "vars", "}"}], ",", 
           RowBox[{"{", "inds", "}"}]}], "}"}], "]"}], "/.", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"{", 
            RowBox[{"var_", ",", "0"}], "}"}], "\[RuleDelayed]", 
           RowBox[{"Sequence", "[", "]"}]}], ",", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"var_", ",", "1"}], "}"}], "\[RuleDelayed]", 
           RowBox[{"{", "var", "}"}]}]}], "}"}]}]}], "]"}]}]}], 
   "]"}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820840353415118*^9, 3.829160465381137*^9},
 CellLabel->"In[5]:=",ExpressionUUID->"0585550f-429a-4a87-b246-6709ff80272b"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"  (CleanSlate) Contexts purged: \"\>", "\[InvisibleSpace]", 
   RowBox[{"{", "\<\"Global`\"\>", "}"}]}],
  SequenceForm["  (CleanSlate) Contexts purged: ", {"Global`"}],
  Editable->False]], "Print",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820840353416061*^9, 3.829146632796653*^9, 
  3.829160157176485*^9, 3.8291604653812847`*^9, 3.829209187217381*^9, 
  3.829239524492804*^9, 3.829240119431374*^9, 3.877792160909122*^9, 
  3.877792208158206*^9, 3.877792700654717*^9, 3.87779401180464*^9, 
  3.8777951875096903`*^9},
 CellLabel->
  "During evaluation of \
In[5]:=",ExpressionUUID->"a316e061-383b-4adf-a0e6-fd3f8b2a60f5"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"  (CleanSlate) Approximate kernel memory recovered: \"\>", 
   "\[InvisibleSpace]", "\<\"11 Kb\"\>"}],
  SequenceForm[
  "  (CleanSlate) Approximate kernel memory recovered: ", "11 Kb"],
  Editable->False]], "Print",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820840353416061*^9, 3.829146632796653*^9, 
  3.829160157176485*^9, 3.8291604653812847`*^9, 3.829209187217381*^9, 
  3.829239524492804*^9, 3.829240119431374*^9, 3.877792160909122*^9, 
  3.877792208158206*^9, 3.877792700654717*^9, 3.87779401180464*^9, 
  3.877795187512863*^9},
 CellLabel->
  "During evaluation of \
In[5]:=",ExpressionUUID->"1685a00d-5891-473f-becf-15faea27d9db"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"\<\"Utilities`CleanSlate`\"\>", 
   ",", "\<\"DocumentationSearch`\"\>", ",", "\<\"ResourceLocator`\"\>", 
   ",", "\<\"NaturalLanguageProcessingLoader`\"\>", ",", "\<\"System`\"\>", 
   ",", "\<\"Global`\"\>"}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820840353416339*^9, 3.829146632805475*^9, 
  3.8291601571818438`*^9, 3.8291604653815403`*^9, 3.8292091872286882`*^9, 
  3.829239524497279*^9, 3.829240119435931*^9, 3.8777921609123096`*^9, 
  3.87779220816188*^9, 3.877792700658255*^9, 3.87779401180866*^9, 
  3.877795187515924*^9},
 CellLabel->"Out[0]=",ExpressionUUID->"d9dfcbd4-f84d-4c7b-8349-3a5698b1bdfe"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"<<", "GeneralRelativityTensors`"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820840353416458*^9, 3.829160465381672*^9},
 CellLabel->"In[2]:=",ExpressionUUID->"a604b8e4-786c-46f3-9ff1-2245f97702e1"],

Cell[BoxData[
 RowBox[{"Needs", "[", "\"\<VariationalMethods`\>\"", "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.829160465381934*^9},
 CellLabel->"In[3]:=",ExpressionUUID->"22cbcd6e-fa88-48b6-b605-1018783c8ae3"]
}, Closed]],

Cell[CellGroupData[{

Cell["Custom Notation", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8225114042235403`*^9, 3.822511435665856*^9}, 
   3.823176577809782*^9, 
   3.82485745570357*^9},ExpressionUUID->"48720785-4b5b-421c-b4a7-\
11424800c40b"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "dtReplace", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dtReplace", " ", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"Dt", "[", "r", "]"}], "\[Rule]", " ", "dr"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "t", "]"}], "\[Rule]", " ", "dt"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "u", "]"}], "\[Rule]", " ", "du"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "v", "]"}], "\[Rule]", " ", "dv"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "x", "]"}], "\[Rule]", " ", "dx"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "y", "]"}], " ", "\[Rule]", " ", "dy"}], " ", ",", 
     " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "z", "]"}], "\[Rule]", " ", "dz"}], " ", ",", " ", 
     "\[IndentingNewLine]", " ", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Theta]", "]"}], " ", "\[Rule]", " ", 
      "d\[Theta]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Phi]", "]"}], " ", "\[Rule]", " ", "d\[Phi]"}], 
     "  ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Eta]", "]"}], " ", "\[Rule]", " ", "d\[Eta]"}], 
     "  ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Chi]", "]"}], "\[Rule]", " ", "d\[Chi]"}], " ", 
     ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Rho]", "]"}], " ", "\[Rule]", " ", "d\[Rho]"}], 
     " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CurlyRho]", "]"}], "\[Rule]", " ", 
      "d\[CurlyRho]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CurlyPhi]", "]"}], " ", "\[Rule]", " ", 
      "d\[CurlyPhi]"}], " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Xi]", "]"}], "\[Rule]", " ", "d\[Xi]"}], " ", ",",
      "  ", "\[IndentingNewLine]", " ", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptT]", "]"}], " ", "\[Rule]", " ", 
      "d\[ScriptT]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptV]", "]"}], "\[Rule]", " ", "d\[ScriptV]"}],
      " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptU]", "]"}], "\[Rule]", " ", "d\[ScriptU]"}],
      " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptX]", "]"}], "\[Rule]", " ", "d\[ScriptX]"}],
      " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptY]", "]"}], "\[Rule]", " ", "d\[ScriptY]"}],
      ",", "   ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptZ]", "]"}], " ", "\[Rule]", " ", 
      "d\[ScriptZ]"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "T", "]"}], "\[Rule]", " ", "dT"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "X", "]"}], "\[Rule]", " ", "dX"}], ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "Y", "]"}], "\[Rule]", " ", "dY"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "Z", "]"}], "\[Rule]", " ", "dZ"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "U", "]"}], "\[Rule]", " ", "dU"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "V", "]"}], "\[Rule]", " ", "dV"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptR]", "]"}], "\[Rule]", " ", "d\[ScriptR]"}],
      "  ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CapitalPhi]", "]"}], "\[Rule]", " ", 
      "d\[CapitalPhi]"}]}], "\[IndentingNewLine]", "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"dtReplace", " ", "//", " ", "TableForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.82317656063256*^9, 3.823176577809904*^9}, {
  3.823598236175474*^9, 3.823598253654046*^9}, {3.823598849383689*^9, 
  3.82359891091936*^9}, {3.8236913141384983`*^9, 3.823691322585009*^9}, {
  3.8237047861092253`*^9, 3.823704790612156*^9}, {3.824032529537923*^9, 
  3.8240325755969877`*^9}, {3.824857446446*^9, 3.824857455703721*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"6ecb8f3a-2655-4f35-8e81-9352fb4f1255"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"Dt", "[", "r", "]"}], "\[Rule]", "dr"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "t", "]"}], "\[Rule]", "dt"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "u", "]"}], "\[Rule]", "du"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "v", "]"}], "\[Rule]", "dv"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "x", "]"}], "\[Rule]", "dx"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "y", "]"}], "\[Rule]", "dy"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "z", "]"}], "\[Rule]", "dz"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Theta]", "]"}], "\[Rule]", "d\[Theta]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Phi]", "]"}], "\[Rule]", "d\[Phi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Eta]", "]"}], "\[Rule]", "d\[Eta]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Chi]", "]"}], "\[Rule]", "d\[Chi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Rho]", "]"}], "\[Rule]", "d\[Rho]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CurlyRho]", "]"}], "\[Rule]", "d\[CurlyRho]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CurlyPhi]", "]"}], "\[Rule]", "d\[CurlyPhi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Xi]", "]"}], "\[Rule]", "d\[Xi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptT]", "]"}], "\[Rule]", "d\[ScriptT]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptV]", "]"}], "\[Rule]", "d\[ScriptV]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptU]", "]"}], "\[Rule]", "d\[ScriptU]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptX]", "]"}], "\[Rule]", "d\[ScriptX]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptY]", "]"}], "\[Rule]", "d\[ScriptY]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptZ]", "]"}], "\[Rule]", "d\[ScriptZ]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "T", "]"}], "\[Rule]", "dT"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "X", "]"}], "\[Rule]", "dX"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "Y", "]"}], "\[Rule]", "dY"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "Z", "]"}], "\[Rule]", "dZ"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "U", "]"}], "\[Rule]", "dU"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "V", "]"}], "\[Rule]", "dV"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptR]", "]"}], "\[Rule]", "d\[ScriptR]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CapitalPhi]", "]"}], "\[Rule]", 
       "d\[CapitalPhi]"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{
  3.82403258232056*^9, 3.8240504355846977`*^9, 3.824051000170314*^9, 
   3.8240514924468307`*^9, 3.8240541728467197`*^9, 3.824054375493238*^9, {
   3.8248574464462023`*^9, 3.8248574557038517`*^9}, 3.829036933622375*^9, 
   3.829209313986479*^9, 3.829239524632103*^9, 3.829240119483301*^9, 
   3.877792160955213*^9, 3.8777922081961823`*^9, 3.877792700689781*^9, 
   3.877794011840826*^9, 3.8777951876544743`*^9},
 CellLabel->
  "Out[6]//TableForm=",ExpressionUUID->"928b6808-4e3e-4da2-9962-f75c85807489"]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"a", "/:", 
    RowBox[{"Dt", "[", "a", "]"}], "=", "0"}], "  ", ";"}], 
  "  "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", " ", "/:", " ", 
    RowBox[{"Dt", "[", "b", "]"}], " ", "=", " ", "0"}], " ", ";"}], 
  "  "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", " ", "/:", " ", 
    RowBox[{"Dt", "[", "c", "]"}], " ", "=", " ", "0"}], " ", ";"}], 
  "  "}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823598195430221*^9, 3.823598210501268*^9}, {
  3.823602495092556*^9, 3.823602530987715*^9}, {3.8236188964036007`*^9, 
  3.8236189207008657`*^9}, {3.8237047330364532`*^9, 3.823704739867001*^9}, {
  3.824857446446303*^9, 3.82485745570395*^9}, {3.877795154501224*^9, 
  3.877795159019952*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"28c33fed-7c50-44a6-ac4f-868f681b2295"]
}, Closed]],

Cell[CellGroupData[{

Cell["Line Element and Metric Functions", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{{3.820937548919169*^9, 3.8209375728447866`*^9}, 
   3.8209383129401073`*^9, 3.8220481344968433`*^9, {3.8225115057038183`*^9, 
   3.822511507783984*^9}, 
   3.822763734568725*^9},ExpressionUUID->"e99f309f-36a0-4b66-9d82-\
288bda8e9e0c"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "lineToMetric", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"lineToMetric", "[", 
    RowBox[{"lineelement_", " ", ",", " ", "differentials_"}], "]"}], ":=", 
   " ", "\[IndentingNewLine]", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"If", "[", 
      RowBox[{
       RowBox[{"i", "\[Equal]", "j"}], " ", ",", 
       RowBox[{"Coefficient", "[", 
        RowBox[{"lineelement", ",", " ", 
         RowBox[{
          RowBox[{"differentials", "[", 
           RowBox[{"[", "i", "]"}], "]"}], " ", 
          RowBox[{"differentials", "[", 
           RowBox[{"[", "j", "]"}], "]"}]}]}], "]"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "/", "2"}], ")"}], "*", 
        RowBox[{"Coefficient", "[", 
         RowBox[{"lineelement", ",", " ", 
          RowBox[{
           RowBox[{"differentials", "[", 
            RowBox[{"[", "i", "]"}], "]"}], " ", 
           RowBox[{"differentials", "[", 
            RowBox[{"[", "j", "]"}], "]"}]}]}], "]"}]}]}], "]"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"i", ",", "1", ",", 
       RowBox[{"Length", "[", "differentials", "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "1", ",", 
       RowBox[{"Length", "[", "differentials", "]"}]}], "}"}]}], "]"}]}], 
  "  ", ";"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{3.821567412203915*^9, 3.821641945174967*^9, 
  3.821641981470141*^9, 3.8220481344970007`*^9, 3.822763734569355*^9},
 CellLabel->"In[10]:=",ExpressionUUID->"7f389239-c788-4969-b90f-baa732652cfa"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "metricToLine", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"metricToLine", "[", 
   RowBox[{"metric_", ",", " ", "differentials_"}], "]"}], ":=", " ", 
  "\[IndentingNewLine]", 
  RowBox[{"Sum", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"metric", "[", 
      RowBox[{"[", 
       RowBox[{"i", ",", "j"}], "]"}], "]"}], " ", 
     RowBox[{"differentials", "[", 
      RowBox[{"[", "i", "]"}], "]"}], " ", 
     RowBox[{"differentials", "[", 
      RowBox[{"[", "j", "]"}], "]"}]}], " ", ",", " ", 
    RowBox[{"{", 
     RowBox[{"i", ",", "1", ",", 
      RowBox[{"Length", "[", "differentials", "]"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "1", ",", 
      RowBox[{"Length", "[", "differentials", "]"}]}], "}"}]}], 
   "]"}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{{3.822762557092309*^9, 3.8227626322008677`*^9}, 
   3.8227637345698223`*^9, 3.822988709740047*^9},
 CellLabel->"In[12]:=",ExpressionUUID->"91dc6abe-f4e8-4b33-b634-1222a2b717c8"]
}, Closed]],

Cell[CellGroupData[{

Cell["Line Element and Metric 1:  Vaidya", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.829240163253091*^9, 3.829240175301499*^9}, {
   3.877792125351472*^9, 3.877792130248012*^9}, {3.877792462794919*^9, 
   3.8777924674110403`*^9}, 3.8777926294745817`*^9, 3.8777939449797993`*^9, {
   3.877794024179883*^9, 
   3.877794025388054*^9}},ExpressionUUID->"9b34d0ec-434b-4cfb-9647-\
3a6262596bf0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"We", " ", "use", " ", "M", " ", "for", " ", "mass"}], ",", " ", 
    RowBox[{"m", " ", "for", " ", "null", " ", "vector"}]}], " ", "*)"}], " ",
   "\[IndentingNewLine]", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Clear", "[", "eq1", "]"}], " ", "\[IndentingNewLine]", 
   RowBox[{"eq1", " ", "=", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"2", "  ", "c", " ", "dr", " ", "dv"}], " ", "-", " ", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "-", 
        FractionBox[
         RowBox[{"2", 
          RowBox[{"M", "[", "v", "]"}]}], "r"]}], ")"}], 
      SuperscriptBox["dv", "2"]}], "+", " ", 
     RowBox[{
      SuperscriptBox["r", "2"], "(", " ", 
      RowBox[{
       SuperscriptBox["d\[Theta]", "2"], "+", " ", 
       RowBox[{
        SuperscriptBox[
         RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], 
        SuperscriptBox["d\[Phi]", "2"]}]}], ")"}], "   ", 
     RowBox[{"(*", " ", 
      RowBox[{"/.", " ", 
       RowBox[{"c", "->", " ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], " ", "Use", " ", "this", " ", "for", " ",
          "outgoing"}]}]}], " ", "*)"}], " "}]}]}]}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.829240064208457*^9, 3.829240104710553*^9}, {
  3.82924013928715*^9, 3.829240168979677*^9}, {3.877792600397051*^9, 
  3.877792627361895*^9}, {3.877794356601368*^9, 3.8777943765771427`*^9}},
 CellLabel->"In[14]:=",ExpressionUUID->"cb79e021-1f9f-4aab-8404-ef4cb5690f5e"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", "c", " ", "dr", " ", "dv"}], "-", 
  RowBox[{
   SuperscriptBox["dv", "2"], " ", 
   RowBox[{"(", 
    RowBox[{"1", "-", 
     FractionBox[
      RowBox[{"2", " ", 
       RowBox[{"M", "[", "v", "]"}]}], "r"]}], ")"}]}], "+", 
  RowBox[{
   SuperscriptBox["r", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     SuperscriptBox["d\[Theta]", "2"], "+", 
     RowBox[{
      SuperscriptBox["d\[Phi]", "2"], " ", 
      SuperscriptBox[
       RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}]}], ")"}]}]}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.829240119537285*^9, 3.829240168979928*^9, 
  3.877792160998032*^9, 3.8777922082371273`*^9, 3.877792638193766*^9, 
  3.877792700732202*^9, 3.877794011882399*^9, 3.877794377962966*^9, 
  3.877795187727187*^9},
 CellLabel->"Out[15]=",ExpressionUUID->"44849638-0d9b-477e-82ea-c2fc6a4239f5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "metric1", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"metric1", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"lineToMetric", "[", " ", 
    RowBox[{"eq1", " ", ",", " ", 
     RowBox[{"{", 
      RowBox[{"dv", ",", "dr", ",", "d\[Theta]", ",", "d\[Phi]"}], "}"}]}], 
    " ", "]"}]}], "  ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"metric1", "  ", "//", " ", "MatrixForm"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.829240123614891*^9, 3.829240137117942*^9}, 
   3.829240168980068*^9, {3.877792120480515*^9, 3.877792121218165*^9}, {
   3.877792225580411*^9, 3.877792248779738*^9}, {3.877792631710382*^9, 
   3.877792636547213*^9}},
 CellLabel->"In[16]:=",ExpressionUUID->"382092ec-474a-41c8-859d-d594c89b724f"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "(", "v", ")"}]}], "r"], "-", "1"}], "c", "0", "0"},
      {"c", "0", "0", "0"},
      {"0", "0", 
       SuperscriptBox["r", "2"], "0"},
      {"0", "0", "0", 
       RowBox[{
        SuperscriptBox["r", "2"], " ", 
        RowBox[{
         SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.829240133204956*^9, 3.829240137451997*^9}, 
   3.829240168980184*^9, 3.87779216101619*^9, 3.877792208254759*^9, 
   3.877792249339374*^9, 3.877792639825091*^9, 3.8777927007528543`*^9, 
   3.877794011901038*^9, 3.8777943800952806`*^9, 3.877795187773539*^9},
 CellLabel->
  "Out[18]//TraditionalForm=",ExpressionUUID->"a8838432-3444-4c09-aca6-\
3e8c1a0f577a"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Calculation of Tensors For Metric 1: Vaidya", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.82083275431255*^9, 3.820832789430361*^9}, {
   3.860242140001411*^9, 3.860242156508766*^9}, {3.864053727271348*^9, 
   3.86405372908741*^9}, {3.877792134599708*^9, 3.877792151254281*^9}, 
   3.877792663379507*^9, {3.877794028603656*^9, 
   3.8777940323557796`*^9}},ExpressionUUID->"60651d99-915e-4e91-8c55-\
5bc06d1bdf5b"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "input", "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"input", "[", 
    RowBox[{
    "equationNumber_", ",", "equation_", ",", "metricName_", ",", 
     "displayName_", ",", "variables_", ",", "indices_"}], "]"}], ":=", " ", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Clear", "[", "tensorList", "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"tensorList", " ", "=", " ", 
       RowBox[{"{", "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"\"\<g\>\"", "<>", "equationNumber"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<christoffel\>\"", "<>", "equationNumber"}], " ", ",", 
         " ", "\[IndentingNewLine]", 
         RowBox[{"\"\<riemann\>\"", "<>", "equationNumber"}], "  ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<ricci\>\"", "<>", "equationNumber"}], " ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<ricciscalar\>\"", "<>", "equationNumber"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<kretschmannscalar\>\"", "<>", "equationNumber"}], "  ", 
         ",", "\[IndentingNewLine]", 
         RowBox[{"\"\<einstein\>\"", "<>", "equationNumber"}], "  ", ",", " ",
          "\[IndentingNewLine]", 
         RowBox[{"\"\<weyl\>\"", "<>", "equationNumber"}], "  ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<cotton\>\"", "<>", "equationNumber"}]}], "  ", 
        "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "1", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"ToMetric", "[", 
        RowBox[{
         RowBox[{"{", " ", 
          RowBox[{"metricName", ",", " ", "displayName"}], " ", "}"}], " ", 
         ",", " ", "variables", ",", " ", "equation", ",", " ", "indices"}], 
        " ", "]"}]}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "  ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{"ChristoffelSymbol", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "3", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RiemannTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWithNested", "\[Rule]", " ", "Simplify"}]}], " ", 
        "]"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "4", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RicciTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "5", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RicciScalar", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "6", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"KretschmannScalar", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "7", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"EinsteinTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       " ", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "8", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"WeylTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", " ", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "9", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"CottonTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960017*^9},
 CellLabel->"In[19]:=",ExpressionUUID->"7801844e-a52e-4fa7-855b-8e105e0b75b3"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
   "Last", " ", "timing", " ", "took", " ", "1.92", " ", "for", " ", "all", 
    " ", "tensors"}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"input", "[", " ", 
    RowBox[{
    "\"\<metric1\>\"", ",", " ", "metric1", ",", " ", "\"\<Vaidya\>\"", ",", 
     "\"\<\!\(\*SuperscriptBox[\(g\), \(vaidya\)]\)\>\"", ",", 
     RowBox[{"{", 
      RowBox[{"v", ",", "r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}], ",", 
     " ", "\"\<Greek\>\""}], "]"}], " ", "//", " ", "Timing"}]}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960153*^9, {3.864053689937333*^9, 3.864053702296399*^9}, {
   3.8777920946250067`*^9, 3.877792114128731*^9}, {3.877792256956819*^9, 
   3.877792259708609*^9}, {3.877792666502596*^9, 3.877792677395349*^9}},
 CellLabel->"In[21]:=",ExpressionUUID->"41cdc62c-941d-4b74-9e22-e6b437da84d8"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"3.476908`", ",", "Null"}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960291*^9, 3.86024212152767*^9, 
  3.864052503462122*^9, 3.8777921610441637`*^9, 3.8777922082838*^9, 
  3.877792254032722*^9, 3.877792702794808*^9, 3.8777940136967993`*^9, 
  3.877794387334272*^9, 3.8777951918371162`*^9},
 CellLabel->"Out[21]=",ExpressionUUID->"c36bbda2-0fd9-4977-9d80-e5598dd2c725"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "1", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "1", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960355*^9, {3.864053556968318*^9, 3.864053582147635*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"1fddb260-c82f-45e2-a39d-9ac2617be5ce"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox[
   SuperscriptBox["g", "vaidya"], "\[Alpha]\[Beta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960409*^9, 3.860242121674992*^9, 3.864052503534184*^9, {
   3.8640535646512403`*^9, 3.864053582420405*^9}, 3.8777921610529633`*^9, 
   3.877792208294853*^9, 3.877792254096753*^9, 3.87779270285006*^9, 
   3.8777940137479553`*^9, 3.877794387381672*^9, 3.877795192002791*^9},
 CellLabel->"Out[22]=",ExpressionUUID->"09fc6cea-2680-4add-9cee-21df7652c6d2"],

Cell[BoxData["\<\"Vaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960409*^9, 3.860242121674992*^9, 3.864052503534184*^9, {
   3.8640535646512403`*^9, 3.864053582420405*^9}, 3.8777921610529633`*^9, 
   3.877792208294853*^9, 3.877792254096753*^9, 3.87779270285006*^9, 
   3.8777940137479553`*^9, 3.877794387381672*^9, 3.87779519200482*^9},
 CellLabel->"Out[23]=",ExpressionUUID->"620032f6-a8f3-4e85-969a-d5b19d6ccedb"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "(", "v", ")"}]}], "r"], "-", "1"}], "c", "0", "0"},
      {"c", "0", "0", "0"},
      {"0", "0", 
       SuperscriptBox["r", "2"], "0"},
      {"0", "0", "0", 
       RowBox[{
        SuperscriptBox["r", "2"], " ", 
        RowBox[{
         SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960409*^9, 3.860242121674992*^9, 3.864052503534184*^9, {
   3.8640535646512403`*^9, 3.864053582420405*^9}, 3.8777921610529633`*^9, 
   3.877792208294853*^9, 3.877792254096753*^9, 3.87779270285006*^9, 
   3.8777940137479553`*^9, 3.877794387381672*^9, 3.8777951920078287`*^9},
 CellLabel->
  "Out[24]//TraditionalForm=",ExpressionUUID->"cf1f162f-9f1f-4606-809d-\
e10ea51e15a7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "2", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "2", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "2", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960476*^9, {3.864053589593115*^9, 3.86405359511217*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"6b4655ff-4f3e-496d-acc3-66a5dd9595bc"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["\[CapitalGamma]", 
   RowBox[{"  ", "\[Beta]\[Gamma]"}], 
   RowBox[{"\[Alpha]", "    "}]],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605*^9, 3.860242121719026*^9, 
  3.8640525035967093`*^9, 3.8640535956915913`*^9, 3.877792161075327*^9, 
  3.877792208320664*^9, 3.8777922541174927`*^9, 3.877792702865546*^9, 
  3.8777940137642193`*^9, 3.8777943873999662`*^9, 3.8777951920200768`*^9},
 CellLabel->"Out[25]=",ExpressionUUID->"f3c0c657-7e9d-4631-afbb-b16fe36ae7e1"],

Cell[BoxData["\<\"ChristoffelSymbolVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605*^9, 3.860242121719026*^9, 
  3.8640525035967093`*^9, 3.8640535956915913`*^9, 3.877792161075327*^9, 
  3.877792208320664*^9, 3.8777922541174927`*^9, 3.877792702865546*^9, 
  3.8777940137642193`*^9, 3.8777943873999662`*^9, 3.8777951920223627`*^9},
 CellLabel->"Out[26]=",ExpressionUUID->"2224f594-4256-4a90-9791-fbd67368700b"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            FractionBox[
             RowBox[{"M", "(", "v", ")"}], 
             RowBox[{"c", " ", 
              SuperscriptBox["r", "2"]}]]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{"-", 
             FractionBox["r", "c"]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"r", " ", 
               RowBox[{
                SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}], "c"]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            FractionBox[
             RowBox[{
              RowBox[{"c", " ", 
               SuperscriptBox["r", "2"], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", "v", ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              RowBox[{"r", " ", 
               RowBox[{"M", "(", "v", ")"}]}], "-", 
              RowBox[{"2", " ", 
               SuperscriptBox[
                RowBox[{"M", "(", "v", ")"}], "2"]}]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "3"]}]]},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"M", "(", "v", ")"}], 
              RowBox[{"c", " ", 
               SuperscriptBox["r", "2"]}]]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"M", "(", "v", ")"}], 
              RowBox[{"c", " ", 
               SuperscriptBox["r", "2"]}]]}]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"r", "-", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], 
              SuperscriptBox["c", "2"]]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{
               RowBox[{
                SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
               RowBox[{"(", 
                RowBox[{"r", "-", 
                 RowBox[{"2", " ", 
                  RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
              SuperscriptBox["c", "2"]]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            FractionBox["1", "r"]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            FractionBox["1", "r"]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             RowBox[{"sin", "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{"-", 
               RowBox[{"cos", "(", "\[Theta]", ")"}]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            FractionBox["1", "r"]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{"cot", "(", "\[Theta]", ")"}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            FractionBox["1", "r"]},
           {
            RowBox[{"cot", "(", "\[Theta]", ")"}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605*^9, 3.860242121719026*^9, 
  3.8640525035967093`*^9, 3.8640535956915913`*^9, 3.877792161075327*^9, 
  3.877792208320664*^9, 3.8777922541174927`*^9, 3.877792702865546*^9, 
  3.8777940137642193`*^9, 3.8777943873999662`*^9, 3.8777951920526447`*^9},
 CellLabel->
  "Out[27]//TraditionalForm=",ExpressionUUID->"d5b91e4a-c207-47ee-a43c-\
4f1faca4372a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "3", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "3", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "3", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.82083274496056*^9, {3.8640535983444366`*^9, 3.86405360358397*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"3e3b2052-7f5e-446f-aae0-14accd33de8e"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["R", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605837`*^9, 3.8602421218754673`*^9, 
  3.8640525038220873`*^9, 3.8640536041026783`*^9, 3.877792161093788*^9, 
  3.877792208340143*^9, 3.877792254171867*^9, 3.8777927029080353`*^9, 
  3.877794013804254*^9, 3.877794387443308*^9, 3.877795192069007*^9},
 CellLabel->"Out[28]=",ExpressionUUID->"73c5c715-f298-477d-8bac-35027341b59d"],

Cell[BoxData["\<\"RiemannTensorVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605837`*^9, 3.8602421218754673`*^9, 
  3.8640525038220873`*^9, 3.8640536041026783`*^9, 3.877792161093788*^9, 
  3.877792208340143*^9, 3.877792254171867*^9, 3.8777927029080353`*^9, 
  3.877794013804254*^9, 3.877794387443308*^9, 3.8777951920711603`*^9},
 CellLabel->"Out[29]=",ExpressionUUID->"ed2ee329-194c-4b3c-a1e4-a27945c80c62"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"2", " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             SuperscriptBox["r", "3"]]}], "0", "0"},
          {
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            SuperscriptBox["r", "3"]], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{"c", " ", 
              SuperscriptBox["r", "2"], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", "v", ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             RowBox[{"r", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "-", 
             RowBox[{"2", " ", 
              SuperscriptBox[
               RowBox[{"M", "(", "v", ")"}], "2"]}]}], 
            RowBox[{
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], "0"},
          {"0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"M", "(", "v", ")"}], 
             RowBox[{"c", " ", "r"}]]}], "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{"c", " ", 
               SuperscriptBox["r", "2"], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", "v", ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              RowBox[{"r", " ", 
               RowBox[{"M", "(", "v", ")"}]}], "-", 
              RowBox[{"2", " ", 
               SuperscriptBox[
                RowBox[{"M", "(", "v", ")"}], "2"]}]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], 
           FractionBox[
            RowBox[{"M", "(", "v", ")"}], 
            RowBox[{"c", " ", "r"}]], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"c", " ", 
                SuperscriptBox["r", "2"], " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", "v", ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"r", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "-", 
               RowBox[{"2", " ", 
                SuperscriptBox[
                 RowBox[{"M", "(", "v", ")"}], "2"]}]}], ")"}]}], 
            RowBox[{
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]]},
          {"0", "0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             RowBox[{"c", " ", "r"}]]}]},
          {"0", "0", "0", "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{"c", " ", 
                 SuperscriptBox["r", "2"], " ", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"M", "(", "v", ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], "+", 
                RowBox[{"r", " ", 
                 RowBox[{"M", "(", "v", ")"}]}], "-", 
                RowBox[{"2", " ", 
                 SuperscriptBox[
                  RowBox[{"M", "(", "v", ")"}], "2"]}]}], ")"}]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            RowBox[{"c", " ", "r"}]], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            SuperscriptBox["r", "3"]], "0", "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{"2", " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             SuperscriptBox["r", "3"]]}], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"M", "(", "v", ")"}], 
             RowBox[{"c", " ", "r"}]]}], "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{"M", "(", "v", ")"}], 
            RowBox[{"c", " ", "r"}]], "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             RowBox[{"c", " ", "r"}]]}]},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            RowBox[{"c", " ", "r"}]], "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{"c", " ", 
               SuperscriptBox["r", "2"], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", "v", ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              RowBox[{"r", " ", 
               RowBox[{"M", "(", "v", ")"}]}], "-", 
              RowBox[{"2", " ", 
               SuperscriptBox[
                RowBox[{"M", "(", "v", ")"}], "2"]}]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], "0"},
          {"0", "0", 
           FractionBox[
            RowBox[{"M", "(", "v", ")"}], 
            RowBox[{"c", " ", "r"}]], "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{"c", " ", 
              SuperscriptBox["r", "2"], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", "v", ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             RowBox[{"r", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "-", 
             RowBox[{"2", " ", 
              SuperscriptBox[
               RowBox[{"M", "(", "v", ")"}], "2"]}]}], 
            RowBox[{
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"M", "(", "v", ")"}], 
             RowBox[{"c", " ", "r"}]]}], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           FractionBox[
            RowBox[{"M", "(", "v", ")"}], 
            RowBox[{"c", " ", "r"}]], "0"},
          {"0", "0", "0", "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{"M", "(", "v", ")"}], 
             RowBox[{"c", " ", "r"}]]}], "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            SuperscriptBox["c", "2"]]},
          {"0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"r", " ", 
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             SuperscriptBox["c", "2"]]}], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{"c", " ", 
                 SuperscriptBox["r", "2"], " ", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"M", "(", "v", ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], "+", 
                RowBox[{"r", " ", 
                 RowBox[{"M", "(", "v", ")"}]}], "-", 
                RowBox[{"2", " ", 
                 SuperscriptBox[
                  RowBox[{"M", "(", "v", ")"}], "2"]}]}], ")"}]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}]},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            RowBox[{"c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"c", " ", 
                SuperscriptBox["r", "2"], " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", "v", ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"r", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "-", 
               RowBox[{"2", " ", 
                SuperscriptBox[
                 RowBox[{"M", "(", "v", ")"}], "2"]}]}], ")"}]}], 
            RowBox[{
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             RowBox[{"c", " ", "r"}]]}], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"M", "(", "v", ")"}]}], 
            RowBox[{"c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"M", "(", "v", ")"}]}], 
             RowBox[{"c", " ", "r"}]]}], "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{"r", " ", 
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             SuperscriptBox["c", "2"]]}]},
          {"0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            SuperscriptBox["c", "2"]], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449605837`*^9, 3.8602421218754673`*^9, 
  3.8640525038220873`*^9, 3.8640536041026783`*^9, 3.877792161093788*^9, 
  3.877792208340143*^9, 3.877792254171867*^9, 3.8777927029080353`*^9, 
  3.877794013804254*^9, 3.877794387443308*^9, 3.877795192193349*^9},
 CellLabel->
  "Out[30]//TraditionalForm=",ExpressionUUID->"95c47167-2925-469f-8168-\
acfad889ac08"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "4", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "4", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "4", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960668*^9, {3.864053607072337*^9, 3.8640536123842278`*^9}},
 CellLabel->"In[31]:=",ExpressionUUID->"1deed3bd-db51-4e7c-a588-c98ddce75e11"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["R", "\[Beta]\[Gamma]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449606943`*^9, 3.860242121928998*^9, 
  3.8640525038931303`*^9, 3.8640536129623747`*^9, 3.877792161117936*^9, 
  3.8777922083689938`*^9, 3.877792254267579*^9, 3.877792703031443*^9, 
  3.8777940139263563`*^9, 3.877794387590517*^9, 3.8777951922138968`*^9},
 CellLabel->"Out[31]=",ExpressionUUID->"8ce388ec-4854-47a1-9ced-5e7e8d9b0a11"],

Cell[BoxData["\<\"RicciTensorVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449606943`*^9, 3.860242121928998*^9, 
  3.8640525038931303`*^9, 3.8640536129623747`*^9, 3.877792161117936*^9, 
  3.8777922083689938`*^9, 3.877792254267579*^9, 3.877792703031443*^9, 
  3.8777940139263563`*^9, 3.877794387590517*^9, 3.87779519221623*^9},
 CellLabel->"Out[32]=",ExpressionUUID->"6f8082c7-c07c-4f24-ba39-f23518409649"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       FractionBox[
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", "v", ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], 
        RowBox[{"c", " ", 
         SuperscriptBox["r", "2"]}]], "0", "0", "0"},
      {"0", "0", "0", "0"},
      {"0", "0", 
       RowBox[{"1", "-", 
        FractionBox["1", 
         SuperscriptBox["c", "2"]]}], "0"},
      {"0", "0", "0", 
       FractionBox[
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
         RowBox[{
          SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}], 
        SuperscriptBox["c", "2"]]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449606943`*^9, 3.860242121928998*^9, 
  3.8640525038931303`*^9, 3.8640536129623747`*^9, 3.877792161117936*^9, 
  3.8777922083689938`*^9, 3.877792254267579*^9, 3.877792703031443*^9, 
  3.8777940139263563`*^9, 3.877794387590517*^9, 3.87779519221968*^9},
 CellLabel->
  "Out[33]//TraditionalForm=",ExpressionUUID->"b07d1831-2772-4371-a40b-\
f4354d9b2aaf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "5", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "5", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "5", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.8208327449607573`*^9, {3.864053615512197*^9, 3.864053620759655*^9}},
 CellLabel->"In[34]:=",ExpressionUUID->"ae0ff631-5b58-486d-aa44-2a6431db8377"],

Cell[BoxData[
 TagBox["\<\"R\"\>",
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.82083274496078*^9, 3.860242121956461*^9, 
  3.86405250393375*^9, 3.8640536213786*^9, 3.877792161136594*^9, 
  3.8777922083940277`*^9, 3.877792254303072*^9, 3.877792703055147*^9, 
  3.877794013950781*^9, 3.877794387621417*^9, 3.877795192246541*^9},
 CellLabel->"Out[34]=",ExpressionUUID->"7415f0a1-243c-4a5f-ad09-1f051ac6d15e"],

Cell[BoxData["\<\"RicciScalarVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.82083274496078*^9, 3.860242121956461*^9, 
  3.86405250393375*^9, 3.8640536213786*^9, 3.877792161136594*^9, 
  3.8777922083940277`*^9, 3.877792254303072*^9, 3.877792703055147*^9, 
  3.877794013950781*^9, 3.877794387621417*^9, 3.877795192249*^9},
 CellLabel->"Out[35]=",ExpressionUUID->"a17f5783-6dbc-4278-a278-d97b4fea073c"],

Cell[BoxData[
 FormBox[
  TagBox[
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["c", "2"], "-", "1"}], ")"}]}], 
    RowBox[{
     SuperscriptBox["c", "2"], " ", 
     SuperscriptBox["r", "2"]}]],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.82083274496078*^9, 3.860242121956461*^9, 
  3.86405250393375*^9, 3.8640536213786*^9, 3.877792161136594*^9, 
  3.8777922083940277`*^9, 3.877792254303072*^9, 3.877792703055147*^9, 
  3.877794013950781*^9, 3.877794387621417*^9, 3.877795192251692*^9},
 CellLabel->
  "Out[36]//TraditionalForm=",ExpressionUUID->"1c403127-496d-4227-8032-\
3feb4829c97a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "6", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "6", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "6", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.82083274496084*^9, {3.8640536234721727`*^9, 3.864053629792131*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"73f96c28-b8c2-494a-97a3-868a96b91db6"],

Cell[BoxData[
 TagBox["\<\"K\"\>",
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960865*^9, 3.8602421219864264`*^9, 
  3.864052503977688*^9, 3.864053630570363*^9, 3.877792161158564*^9, 
  3.877792208419393*^9, 3.877792254321981*^9, 3.87779270306983*^9, 
  3.877794013965366*^9, 3.8777943876527147`*^9, 3.877795192263649*^9},
 CellLabel->"Out[37]=",ExpressionUUID->"864e4815-ccce-4a7e-9da5-9bc984194fd6"],

Cell[BoxData["\<\"KretschmannScalarVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960865*^9, 3.8602421219864264`*^9, 
  3.864052503977688*^9, 3.864053630570363*^9, 3.877792161158564*^9, 
  3.877792208419393*^9, 3.877792254321981*^9, 3.87779270306983*^9, 
  3.877794013965366*^9, 3.8777943876527147`*^9, 3.877795192266183*^9},
 CellLabel->"Out[38]=",ExpressionUUID->"317f48ee-208c-4f3f-aa21-d1df28a7ed4f"],

Cell[BoxData[
 FormBox[
  TagBox[
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"4", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r", " ", 
        RowBox[{"M", "(", "v", ")"}]}], "+", 
       RowBox[{
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["c", "2"], "-", "1"}], ")"}], "2"], " ", 
        SuperscriptBox["r", "2"]}], "+", 
       RowBox[{"12", " ", 
        SuperscriptBox[
         RowBox[{"M", "(", "v", ")"}], "2"]}]}], ")"}]}], 
    RowBox[{
     SuperscriptBox["c", "4"], " ", 
     SuperscriptBox["r", "6"]}]],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960865*^9, 3.8602421219864264`*^9, 
  3.864052503977688*^9, 3.864053630570363*^9, 3.877792161158564*^9, 
  3.877792208419393*^9, 3.877792254321981*^9, 3.87779270306983*^9, 
  3.877794013965366*^9, 3.8777943876527147`*^9, 3.8777951922691097`*^9},
 CellLabel->
  "Out[39]//TraditionalForm=",ExpressionUUID->"2a26cfee-e39d-4599-b150-\
615681a59737"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "7", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "7", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "7", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744960927*^9, {3.864053633984446*^9, 3.864053641391756*^9}},
 CellLabel->"In[40]:=",ExpressionUUID->"b996a705-b105-4f36-a838-ebcbd2d69028"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["G", "\[Alpha]\[Beta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960959*^9, 3.860242122044949*^9, 
  3.8640525040615273`*^9, 3.864053642202518*^9, 3.8777921611751833`*^9, 
  3.8777922084412937`*^9, 3.877792254355235*^9, 3.877792703091267*^9, 
  3.877794013990653*^9, 3.877794387669647*^9, 3.877795192294272*^9},
 CellLabel->"Out[40]=",ExpressionUUID->"98310f91-ca83-4f95-bf2d-cec5f43f0a75"],

Cell[BoxData["\<\"EinsteinTensorVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960959*^9, 3.860242122044949*^9, 
  3.8640525040615273`*^9, 3.864053642202518*^9, 3.8777921611751833`*^9, 
  3.8777922084412937`*^9, 3.877792254355235*^9, 3.877792703091267*^9, 
  3.877794013990653*^9, 3.877794387669647*^9, 3.8777951922973137`*^9},
 CellLabel->"Out[41]=",ExpressionUUID->"adf18f83-d26a-485f-9fdc-3bf36095e917"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       FractionBox[
        RowBox[{
         RowBox[{"r", " ", 
          RowBox[{"(", 
           RowBox[{
            SuperscriptBox["c", "2"], "+", 
            RowBox[{"2", " ", "c", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", "v", ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None]}], "-", "1"}], ")"}]}], "-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
          RowBox[{"M", "(", "v", ")"}]}]}], 
        RowBox[{
         SuperscriptBox["c", "2"], " ", 
         SuperscriptBox["r", "3"]}]], 
       FractionBox[
        RowBox[{"1", "-", 
         SuperscriptBox["c", "2"]}], 
        RowBox[{"c", " ", 
         SuperscriptBox["r", "2"]}]], "0", "0"},
      {
       FractionBox[
        RowBox[{"1", "-", 
         SuperscriptBox["c", "2"]}], 
        RowBox[{"c", " ", 
         SuperscriptBox["r", "2"]}]], "0", "0", "0"},
      {"0", "0", "0", "0"},
      {"0", "0", "0", "0"}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744960959*^9, 3.860242122044949*^9, 
  3.8640525040615273`*^9, 3.864053642202518*^9, 3.8777921611751833`*^9, 
  3.8777922084412937`*^9, 3.877792254355235*^9, 3.877792703091267*^9, 
  3.877794013990653*^9, 3.877794387669647*^9, 3.877795192300702*^9},
 CellLabel->
  "Out[42]//TraditionalForm=",ExpressionUUID->"9d87ee65-7619-4f7a-9624-\
20da664b0726"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "8", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "8", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "8", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.8208327449610243`*^9, {3.864053645904397*^9, 3.8640536513523817`*^9}},
 CellLabel->"In[43]:=",ExpressionUUID->"ae7ca38a-25ce-4411-8113-58e7489f028a"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744961051*^9, 3.860242122628749*^9, 
  3.864052504856409*^9, 3.864053652404649*^9, 3.877792161196949*^9, 
  3.8777922084678383`*^9, 3.8777922543744183`*^9, 3.877792703106175*^9, 
  3.877794014009095*^9, 3.877794387710382*^9, 3.877795192314128*^9},
 CellLabel->"Out[43]=",ExpressionUUID->"9293acdf-6420-4243-8391-f3c2e03798f3"],

Cell[BoxData["\<\"WeylTensorVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744961051*^9, 3.860242122628749*^9, 
  3.864052504856409*^9, 3.864053652404649*^9, 3.877792161196949*^9, 
  3.8777922084678383`*^9, 3.8777922543744183`*^9, 3.877792703106175*^9, 
  3.877794014009095*^9, 3.877794387710382*^9, 3.8777951923176622`*^9},
 CellLabel->"Out[44]=",ExpressionUUID->"c67ec192-4982-4e57-91c6-d74301731bf5"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"3", " ", 
             SuperscriptBox["r", "3"]}]], "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["r", "3"]}]], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{"(", 
              RowBox[{"r", "-", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", 
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], "0"},
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{"(", 
               RowBox[{"r", "-", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"6", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             RowBox[{"6", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], 
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{"r", "-", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", 
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]]},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{"r", "-", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"6", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             RowBox[{"6", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["r", "3"]}]], "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"3", " ", 
             SuperscriptBox["r", "3"]}]], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{"(", 
               RowBox[{"r", "-", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"6", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             RowBox[{"6", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}], "0"},
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{"(", 
              RowBox[{"r", "-", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", 
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], "+", 
             
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["c", "2"], " ", 
              RowBox[{"(", 
               RowBox[{"-", "r"}], ")"}]}], "-", 
             RowBox[{"6", " ", 
              RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["c", "2"]}]]},
          {"0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["c", "2"]}]], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{"-", 
            FractionBox[
             RowBox[{
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              RowBox[{"(", 
               RowBox[{"r", "-", 
                RowBox[{"2", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
                "+", 
                RowBox[{"6", " ", 
                 RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
             RowBox[{"6", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "2"]}]]}]},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{"r", "-", 
               RowBox[{"2", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", 
             SuperscriptBox["c", "2"], " ", 
             SuperscriptBox["r", "2"]}]], 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]]},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {
           FractionBox[
            RowBox[{
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"6", " ", "c", " ", "r"}]], "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                SuperscriptBox["c", "2"], " ", 
                RowBox[{"(", 
                 RowBox[{"-", "r"}], ")"}]}], "-", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}], "+", "r"}], ")"}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["c", "2"]}]]},
          {"0", "0", 
           FractionBox[
            RowBox[{"r", " ", 
             RowBox[{
              SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                RowBox[{"(", 
                 RowBox[{
                  SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", "r"}], 
               "+", 
               RowBox[{"6", " ", 
                RowBox[{"M", "(", "v", ")"}]}]}], ")"}]}], 
            RowBox[{"3", " ", 
             SuperscriptBox["c", "2"]}]], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.820832744961051*^9, 3.860242122628749*^9, 
  3.864052504856409*^9, 3.864053652404649*^9, 3.877792161196949*^9, 
  3.8777922084678383`*^9, 3.8777922543744183`*^9, 3.877792703106175*^9, 
  3.877794014009095*^9, 3.877794387710382*^9, 3.87779519250749*^9},
 CellLabel->
  "Out[45]//TraditionalForm=",ExpressionUUID->"b1107e3d-5677-444b-99f5-\
8d0b55455e37"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"tensorList", "[", 
  RowBox[{"[", "9", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"TensorName", "[", 
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "9", "]"}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "9", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820832744961113*^9, {3.8640536558957033`*^9, 3.864053660951818*^9}},
 CellLabel->"In[46]:=",ExpressionUUID->"89764af5-ff84-49a4-b275-ad5811bc5eae"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449611397`*^9, 3.8602421232521753`*^9, 
  3.8640525057539186`*^9, 3.8640536618179703`*^9, 3.8777921612155457`*^9, 
  3.87779220848667*^9, 3.87779225446626*^9, 3.877792703209371*^9, 
  3.877794014113894*^9, 3.877794387930554*^9, 3.8777951925296803`*^9},
 CellLabel->"Out[46]=",ExpressionUUID->"5b6d9312-1981-4115-bfe6-93e9e38e457a"],

Cell[BoxData["\<\"CottonTensorVaidya\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449611397`*^9, 3.8602421232521753`*^9, 
  3.8640525057539186`*^9, 3.8640536618179703`*^9, 3.8777921612155457`*^9, 
  3.87779220848667*^9, 3.87779225446626*^9, 3.877792703209371*^9, 
  3.877794014113894*^9, 3.877794387930554*^9, 3.877795192532751*^9},
 CellLabel->"Out[47]=",ExpressionUUID->"8e8e5841-d1ff-4db5-b186-9b54308a90a1"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            FractionBox[
             RowBox[{
              RowBox[{"4", " ", 
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
               RowBox[{"M", "(", "v", ")"}]}], "-", 
              RowBox[{"2", " ", "r", " ", 
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "+", 
                 RowBox[{"6", " ", "c", " ", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", "v", ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], "-", "1"}], ")"}]}]}], 
             RowBox[{"3", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "4"]}]]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            FractionBox[
             RowBox[{
              RowBox[{"2", " ", "r", " ", 
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "+", 
                 RowBox[{"6", " ", "c", " ", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", "v", ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], "-", "1"}], ")"}]}], "-", 
              RowBox[{"4", " ", 
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
               RowBox[{"M", "(", "v", ")"}]}]}], 
             RowBox[{"3", " ", 
              SuperscriptBox["c", "2"], " ", 
              SuperscriptBox["r", "4"]}]]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            FractionBox[
             RowBox[{"2", " ", 
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}]}], 
             RowBox[{"3", " ", "c", " ", 
              SuperscriptBox["r", "3"]}]]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "-", "1"}], ")"}]}], 
              RowBox[{"3", " ", "c", " ", 
               SuperscriptBox["r", "3"]}]]}]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            FractionBox[
             RowBox[{"2", " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", "v", ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", "r"}]]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            FractionBox[
             RowBox[{
              SuperscriptBox["c", "2"], "-", "1"}], 
             RowBox[{"3", " ", 
              SuperscriptBox["c", "2"], " ", "r"}]]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", "v", ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], 
              RowBox[{
               SuperscriptBox["c", "2"], " ", "r"}]]}]},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["c", "2"], "-", "1"}], 
              RowBox[{"3", " ", 
               SuperscriptBox["c", "2"], " ", "r"}]]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            FractionBox[
             RowBox[{"2", " ", 
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", "v", ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], 
             RowBox[{
              SuperscriptBox["c", "2"], " ", "r"}]]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            FractionBox[
             RowBox[{
              RowBox[{"(", 
               RowBox[{
                SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
              RowBox[{
               SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}], 
             RowBox[{"3", " ", 
              SuperscriptBox["c", "2"], " ", "r"}]]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"2", " ", 
               RowBox[{
                SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", "v", ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], 
              RowBox[{
               SuperscriptBox["c", "2"], " ", "r"}]]}]},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{
               RowBox[{"(", 
                RowBox[{
                 SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
               RowBox[{
                SuperscriptBox["sin", "2"], "(", "\[Theta]", ")"}]}], 
              RowBox[{"3", " ", 
               SuperscriptBox["c", "2"], " ", "r"}]]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8208327449611397`*^9, 3.8602421232521753`*^9, 
  3.8640525057539186`*^9, 3.8640536618179703`*^9, 3.8777921612155457`*^9, 
  3.87779220848667*^9, 3.87779225446626*^9, 3.877792703209371*^9, 
  3.877794014113894*^9, 3.877794387930554*^9, 3.877795192581994*^9},
 CellLabel->
  "Out[48]//TraditionalForm=",ExpressionUUID->"f5d13578-d8ff-468f-96b5-\
183d55274dc1"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Derivation of Vacuum Field Equations For Metric 1: Vaidya", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.855773448192749*^9, 3.8557734613620567`*^9}, {
  3.863953567514872*^9, 3.863953580186605*^9}, {3.877794040811727*^9, 
  3.877794041282007*^9}},ExpressionUUID->"c188ac9d-8f87-451c-8e6b-\
4138386107c2"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "nonzeroRicci", "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroRicci", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"DeleteDuplicates", "[", 
    RowBox[{"Cases", "[", " ", 
     RowBox[{
      RowBox[{"Flatten", "[", 
       RowBox[{"Table", "[", 
        RowBox[{
         RowBox[{"If", "[", " ", 
          RowBox[{
           RowBox[{"i", "<=", " ", "j"}], " ", ",", " ", 
           RowBox[{
            RowBox[{"TensorValues", "[", 
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
            RowBox[{"[", 
             RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", "Nothing"}], "]"}], 
         " ", ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", "1", ",", "4"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"j", ",", "1", ",", "4"}], "}"}]}], "]"}], "]"}], " ", ",", 
      " ", 
      RowBox[{"Except", "[", "0", "]"}]}], "]"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"nonzeroRicci", " ", "//", " ", "TableForm", " "}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8550804551055307`*^9, 3.855080461809052*^9}, 
   3.855773453961225*^9, {3.863953582622657*^9, 3.863953589603964*^9}, {
   3.877792719494606*^9, 3.877792725230019*^9}, 3.8777928373559303`*^9},
 CellLabel->"In[49]:=",ExpressionUUID->"c9e8bd40-a47c-4e4c-86d6-aadcbf669410"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      FractionBox[
       RowBox[{"2", " ", 
        RowBox[{
         SuperscriptBox["M", "\[Prime]",
          MultilineFunction->None], "[", "v", "]"}]}], 
       RowBox[{"c", " ", 
        SuperscriptBox["r", "2"]}]]},
     {
      RowBox[{"1", "-", 
       FractionBox["1", 
        SuperscriptBox["c", "2"]]}]},
     {
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          SuperscriptBox["c", "2"]}], ")"}], " ", 
        SuperscriptBox[
         RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}], 
       SuperscriptBox["c", "2"]]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.877792703324074*^9, 3.877792726531089*^9}, 
   3.877792837630652*^9, 3.877794014152884*^9, 3.877794387990775*^9, 
   3.877795192615464*^9},
 CellLabel->
  "Out[51]//TableForm=",ExpressionUUID->"56f5e224-1d86-4a4b-b4f0-\
146b13add967"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "nonzeroEinstein", "]"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroEinstein", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"DeleteDuplicates", "[", 
    RowBox[{"Cases", "[", " ", 
     RowBox[{
      RowBox[{"Flatten", "[", 
       RowBox[{"Table", "[", 
        RowBox[{
         RowBox[{"If", "[", " ", 
          RowBox[{
           RowBox[{"i", "<=", " ", "j"}], " ", ",", " ", 
           RowBox[{
            RowBox[{"TensorValues", "[", 
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
            RowBox[{"[", 
             RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", "Nothing"}], "]"}], 
         " ", ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", "1", ",", "4"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"j", ",", "1", ",", "4"}], "}"}]}], "]"}], "]"}], " ", ",", 
      " ", 
      RowBox[{"Except", "[", "0", "]"}]}], "]"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroEinstein", " ", "//", " ", "TableForm"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8550804645210114`*^9, 3.855080470568581*^9}, 
   3.855773453961347*^9, {3.8639535911097507`*^9, 3.863953596755208*^9}, {
   3.877792729749896*^9, 3.877792734606649*^9}},
 CellLabel->"In[52]:=",ExpressionUUID->"38aa22b9-9624-403f-8545-c4c6f4ac9a68"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       FractionBox[
        RowBox[{
         RowBox[{"r", " ", 
          RowBox[{"(", 
           RowBox[{
            SuperscriptBox["c", "2"], "+", 
            RowBox[{"2", " ", "c", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", "v", ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None]}], "-", "1"}], ")"}]}], "-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            SuperscriptBox["c", "2"], "-", "1"}], ")"}], " ", 
          RowBox[{"M", "(", "v", ")"}]}]}], 
        RowBox[{
         SuperscriptBox["c", "2"], " ", 
         SuperscriptBox["r", "3"]}]]},
      {
       FractionBox[
        RowBox[{"1", "-", 
         SuperscriptBox["c", "2"]}], 
        RowBox[{"c", " ", 
         SuperscriptBox["r", "2"]}]]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.877792703338645*^9, 3.87779273490799*^9, 
  3.877794014171056*^9, 3.8777943880155497`*^9, 3.877795192647788*^9},
 CellLabel->
  "Out[54]//TraditionalForm=",ExpressionUUID->"03fd4318-860b-453d-af42-\
e21de6ce7954"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Euler Lagrange Equations Giving Equations 3 and 4", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8434096837525587`*^9, 3.84340969900767*^9}, {
   3.84779815072215*^9, 3.847798172222159*^9}, 3.847798208161132*^9, {
   3.877795076171809*^9, 
   3.8777950819964733`*^9}},ExpressionUUID->"24a5e37c-8886-4ee6-a108-\
08e6ba91ba59"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eulerLagrangeEquations", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"eulerLagrangeEquations", "[", 
    RowBox[{"metric_", ",", " ", "variables_", " ", ",", " ", "parameter_"}], 
    " ", "]"}], ":=", " ", 
   RowBox[{"Module", "[", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"qReplace", ",", "eqs", ",", "eulerEquations"}], "}"}], " ", 
     ",", "\[IndentingNewLine]", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Clear", "[", "q", "]"}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{"q", " ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{"Flatten", "[", 
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{"Map", "[", 
           RowBox[{
            RowBox[{"variables", "[", 
             RowBox[{"[", "i", "]"}], "]"}], ",", 
            RowBox[{"{", "parameter", "}"}]}], "]"}], " ", ",", " ", 
          RowBox[{"{", 
           RowBox[{"i", ",", "1", ",", 
            RowBox[{"Length", "[", "variables", "]"}]}], "}"}]}], "]"}], 
        "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"Clear", "[", "qReplace", "]"}], " ", ";", 
      "\[IndentingNewLine]", 
      RowBox[{"qReplace", " ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{"Thread", "[", 
        RowBox[{"variables", " ", "\[Rule]", " ", "q"}], " ", "]"}]}], " ", 
      ";", "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"Clear", "[", "\[ScriptCapitalL]", "]"}], " ", ";", 
      "\[IndentingNewLine]", 
      RowBox[{"\[ScriptCapitalL]", " ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{"Sum", "[", 
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{"metric", " ", "/.", " ", "qReplace"}], ")"}], "[", 
           RowBox[{"[", 
            RowBox[{"i", ",", "j"}], "]"}], "]"}], " ", "*", "   ", 
          RowBox[{
           RowBox[{"D", "[", 
            RowBox[{"q", ",", "parameter"}], "]"}], "[", 
           RowBox[{"[", "i", "]"}], "]"}], " ", 
          RowBox[{
           RowBox[{"D", "[", 
            RowBox[{"q", ",", "parameter"}], "]"}], "[", 
           RowBox[{"[", "j", "]"}], "]"}]}], " ", ",", " ", 
         RowBox[{"{", 
          RowBox[{"i", ",", "1", ",", " ", 
           RowBox[{"Length", "[", "q", "]"}]}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"j", ",", "1", ",", 
           RowBox[{"Length", "[", "q", "]"}]}], "}"}]}], "]"}]}], " ", ";", 
      "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"Clear", "[", "eqs", "]"}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{"eqs", " ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{"D", "[", " ", 
              RowBox[{
               RowBox[{"D", "[", " ", 
                RowBox[{"\[ScriptCapitalL]", " ", ",", "  ", 
                 RowBox[{
                  SubscriptBox["\[PartialD]", "parameter"], 
                  RowBox[{"q", "[", 
                   RowBox[{"[", "i", "]"}], "]"}]}]}], "]"}], " ", ",", " ", 
               "parameter"}], " ", "]"}], " ", "-", 
             RowBox[{"D", "[", " ", 
              RowBox[{"\[ScriptCapitalL]", " ", ",", "  ", 
               RowBox[{"q", "[", 
                RowBox[{"[", "i", "]"}], "]"}]}], "]"}]}], " ", ")"}], "==", 
           "0"}], "  ", ",", " ", 
          RowBox[{"{", 
           RowBox[{"i", ",", "1", ",", 
            RowBox[{"Length", "[", "q", "]"}]}], "}"}]}], "]"}], " ", "//", 
        " ", "Expand"}]}], "   ", ";", "\[IndentingNewLine]", 
      "\[IndentingNewLine]", 
      RowBox[{"Clear", "[", "eulerEquations", "]"}], " ", ";", 
      "\[IndentingNewLine]", 
      RowBox[{"eulerEquations", " ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"Flatten", "[", 
         RowBox[{"Solve", "[", " ", 
          RowBox[{"eqs", " ", ",", " ", 
           RowBox[{"D", "[", 
            RowBox[{"q", ",", 
             RowBox[{"{", 
              RowBox[{"parameter", ",", "2"}], "}"}]}], "]"}]}], "]"}], " ", 
         "]"}], " ", "/.", " ", 
        RowBox[{"Rule", "->", " ", "Equal"}]}]}]}]}], " ", 
    "\[IndentingNewLine]", "\[IndentingNewLine]", "]"}]}], ";"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{
  3.843409690313745*^9, {3.8477972356055098`*^9, 3.8477973009543877`*^9}, {
   3.847802455955916*^9, 3.84780245637819*^9}, {3.847802572588552*^9, 
   3.8478025789311523`*^9}, {3.848001245938334*^9, 3.848001253401595*^9}, {
   3.848002025103499*^9, 3.848002030352234*^9}, {3.877793422707035*^9, 
   3.877793422915902*^9}, {3.877793552344739*^9, 3.8777935528742123`*^9}},
 CellLabel->"In[77]:=",ExpressionUUID->"9be93aa5-d7d4-4bc4-8819-1b1010270f8e"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
    "To", " ", "get", " ", "rid", " ", "of", " ", "the", " ", "functional", 
     " ", "dependence", " ", "on", " ", "\[Lambda]", " ", "after", " ", 
     "computing", " ", "the", " ", "geodesic", " ", "equations", " ", "try", 
     " ", "useing", " ", 
     RowBox[{"this", ":"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", "/.", 
    RowBox[{
     RowBox[{"q_", "[", "\[Lambda]", "]"}], " ", "\[RuleDelayed]", " ", 
     "q"}]}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], 
  " "}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.847896169314475*^9, 3.847896200976667*^9}},
 CellLabel->"In[79]:=",ExpressionUUID->"5a8a932e-228b-4f7f-8a53-19e35bea8d83"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "geodesicEquationsMetric1", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"geodesicEquationsMetric1", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"eulerLagrangeEquations", "[", 
     RowBox[{"metric1", ",", 
      RowBox[{"{", 
       RowBox[{"v", ",", "r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}], ",", 
      "\[Lambda]"}], "]"}], "  ", "//", " ", "Expand"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"geodesicEquationsMetric1", " ", "//", " ", "TableForm"}]}], "Input",\

 CellChangeTimes->{{3.87779338895784*^9, 3.8777934132146883`*^9}, {
  3.877793443654162*^9, 3.877793465526527*^9}},
 CellLabel->"In[80]:=",ExpressionUUID->"a1707b9d-b200-4115-98fb-7f1c9ff75d11"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{
        SuperscriptBox["v", "\[Prime]\[Prime]",
         MultilineFunction->None], "[", "\[Lambda]", "]"}], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{
           RowBox[{"M", "[", 
            RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
           SuperscriptBox[
            RowBox[{
             SuperscriptBox["v", "\[Prime]",
              MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
          RowBox[{"c", " ", 
           SuperscriptBox[
            RowBox[{"r", "[", "\[Lambda]", "]"}], "2"]}]]}], "+", 
        FractionBox[
         RowBox[{
          RowBox[{"r", "[", "\[Lambda]", "]"}], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], "c"], 
        "+", 
        FractionBox[
         RowBox[{
          RowBox[{"r", "[", "\[Lambda]", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", 
            RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         "c"]}]}]},
     {
      RowBox[{
       RowBox[{
        SuperscriptBox["r", "\[Prime]\[Prime]",
         MultilineFunction->None], "[", "\[Lambda]", "]"}], "\[Equal]", 
       RowBox[{
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", 
           RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
          RowBox[{
           SuperscriptBox["r", "\[Prime]",
            MultilineFunction->None], "[", "\[Lambda]", "]"}], " ", 
          RowBox[{
           SuperscriptBox["v", "\[Prime]",
            MultilineFunction->None], "[", "\[Lambda]", "]"}]}], 
         RowBox[{"c", " ", 
          SuperscriptBox[
           RowBox[{"r", "[", "\[Lambda]", "]"}], "2"]}]], "+", 
        FractionBox[
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"M", "[", 
            RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox[
           RowBox[{"r", "[", "\[Lambda]", "]"}], "3"]}]], "-", 
        FractionBox[
         RowBox[{
          RowBox[{"M", "[", 
           RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox[
           RowBox[{"r", "[", "\[Lambda]", "]"}], "2"]}]], "-", 
        FractionBox[
         RowBox[{
          RowBox[{
           SuperscriptBox["M", "\[Prime]",
            MultilineFunction->None], "[", 
           RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         RowBox[{"c", " ", 
          RowBox[{"r", "[", "\[Lambda]", "]"}]}]], "-", 
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", 
           RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         SuperscriptBox["c", "2"]], "+", 
        FractionBox[
         RowBox[{
          RowBox[{"r", "[", "\[Lambda]", "]"}], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         SuperscriptBox["c", "2"]], "-", 
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", 
           RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}], " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", 
            RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         SuperscriptBox["c", "2"]], "+", 
        FractionBox[
         RowBox[{
          RowBox[{"r", "[", "\[Lambda]", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", 
            RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], 
         SuperscriptBox["c", "2"]]}]}]},
     {
      RowBox[{
       RowBox[{
        SuperscriptBox["\[Theta]", "\[Prime]\[Prime]",
         MultilineFunction->None], "[", "\[Lambda]", "]"}], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{"2", " ", 
           RowBox[{
            SuperscriptBox["r", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], " ", 
           RowBox[{
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}]}], 
          RowBox[{"r", "[", "\[Lambda]", "]"}]]}], "+", 
        RowBox[{
         RowBox[{"Cos", "[", 
          RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], " ", 
         RowBox[{"Sin", "[", 
          RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], " ", 
         SuperscriptBox[
          RowBox[{
           SuperscriptBox["\[Phi]", "\[Prime]",
            MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}]}]}]},
     {
      RowBox[{
       RowBox[{
        SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
         MultilineFunction->None], "[", "\[Lambda]", "]"}], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{"2", " ", 
           RowBox[{
            SuperscriptBox["r", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}], " ", 
           RowBox[{
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], "[", "\[Lambda]", "]"}]}], 
          RowBox[{"r", "[", "\[Lambda]", "]"}]]}], "-", 
        RowBox[{"2", " ", 
         RowBox[{"Cot", "[", 
          RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], " ", 
         RowBox[{
          SuperscriptBox["\[Theta]", "\[Prime]",
           MultilineFunction->None], "[", "\[Lambda]", "]"}], " ", 
         RowBox[{
          SuperscriptBox["\[Phi]", "\[Prime]",
           MultilineFunction->None], "[", "\[Lambda]", "]"}]}]}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.877793413870743*^9, 3.877793465801942*^9}, 
   3.877793558107403*^9, 3.877794014593544*^9, 3.877794388472617*^9, 
   3.877795193180305*^9},
 CellLabel->
  "Out[82]//TableForm=",ExpressionUUID->"508074b0-9cb0-4559-aa59-\
7944efe07379"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "geodesicEquationsMetric1Simplified", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
  "geodesicEquationsMetric1Simplified", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"geodesicEquationsMetric1", " ", "/.", " ", 
    RowBox[{
     RowBox[{"q_", "[", "\[Lambda]", "]"}], " ", "\[RuleDelayed]", " ", 
     "q"}]}]}], "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"geodesicEquationsMetric1Simplified", " ", "//", " ", "TableForm", 
  " "}]}], "Input",
 CellChangeTimes->{{3.877793480789935*^9, 3.8777934868047647`*^9}, {
  3.8777935693558292`*^9, 3.877793573566175*^9}, {3.877794100800078*^9, 
  3.8777941278075037`*^9}},
 CellLabel->"In[83]:=",ExpressionUUID->"f267e8fc-024c-4eda-b315-1d8b81c38de1"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       SuperscriptBox["v", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{
           RowBox[{"M", "[", "v", "]"}], " ", 
           SuperscriptBox[
            RowBox[{"(", 
             SuperscriptBox["v", "\[Prime]",
              MultilineFunction->None], ")"}], "2"]}], 
          RowBox[{"c", " ", 
           SuperscriptBox["r", "2"]}]]}], "+", 
        FractionBox[
         RowBox[{"r", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], "c"], "+", 
        FractionBox[
         RowBox[{"r", " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], "c"]}]}]},
     {
      RowBox[{
       SuperscriptBox["r", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox["r", "\[Prime]",
           MultilineFunction->None], " ", 
          SuperscriptBox["v", "\[Prime]",
           MultilineFunction->None]}], 
         RowBox[{"c", " ", 
          SuperscriptBox["r", "2"]}]], "-", 
        FractionBox[
         RowBox[{
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox["r", "2"]}]], "+", 
        FractionBox[
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"M", "[", "v", "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox["r", "3"]}]], "+", 
        FractionBox[
         RowBox[{"r", " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         SuperscriptBox["c", "2"]], "-", 
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Theta]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         SuperscriptBox["c", "2"]], "+", 
        FractionBox[
         RowBox[{"r", " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         SuperscriptBox["c", "2"]], "-", 
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["\[Phi]", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         SuperscriptBox["c", "2"]], "-", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"], " ", 
          RowBox[{
           SuperscriptBox["M", "\[Prime]",
            MultilineFunction->None], "[", "v", "]"}]}], 
         RowBox[{"c", " ", "r"}]]}]}]},
     {
      RowBox[{
       SuperscriptBox["\[Theta]", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{"2", " ", 
           SuperscriptBox["r", "\[Prime]",
            MultilineFunction->None], " ", 
           SuperscriptBox["\[Theta]", "\[Prime]",
            MultilineFunction->None]}], "r"]}], "+", 
        RowBox[{
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           SuperscriptBox["\[Phi]", "\[Prime]",
            MultilineFunction->None], ")"}], "2"]}]}]}]},
     {
      RowBox[{
       SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{
        RowBox[{"-", 
         FractionBox[
          RowBox[{"2", " ", 
           SuperscriptBox["r", "\[Prime]",
            MultilineFunction->None], " ", 
           SuperscriptBox["\[Phi]", "\[Prime]",
            MultilineFunction->None]}], "r"]}], "-", 
        RowBox[{"2", " ", 
         RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", 
         SuperscriptBox["\[Theta]", "\[Prime]",
          MultilineFunction->None], " ", 
         SuperscriptBox["\[Phi]", "\[Prime]",
          MultilineFunction->None]}]}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.877793479338393*^9, 3.877793487285523*^9}, {
   3.8777935604426603`*^9, 3.877793573954935*^9}, 3.877794014606214*^9, 
   3.877794128500355*^9, 3.8777943884908*^9, 3.8777951931929197`*^9},
 CellLabel->
  "Out[85]//TableForm=",ExpressionUUID->"d850120c-3b1e-4ed3-8c4b-\
0e139ede8e47"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "firstIntegrals", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"firstIntegrals", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"FirstIntegrals", "[", " ", 
    RowBox[{
    "\[ScriptCapitalL]", " ", ",", " ", "q", " ", ",", " ", "\[Lambda]"}], 
    " ", "]"}]}], "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"firstIntegrals", "//", " ", "TableForm"}]}], "Input",
 CellLabel->"In[86]:=",ExpressionUUID->"db7becd4-1e02-4026-b6c0-9ced2044d356"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"FirstIntegral", "[", "\[Phi]", "]"}], "\[Rule]", 
       RowBox[{
        RowBox[{"-", "2"}], " ", 
        SuperscriptBox[
         RowBox[{"r", "[", "\[Lambda]", "]"}], "2"], " ", 
        SuperscriptBox[
         RowBox[{"Sin", "[", 
          RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
        RowBox[{
         SuperscriptBox["\[Phi]", "\[Prime]",
          MultilineFunction->None], "[", "\[Lambda]", "]"}]}]}]},
     {
      RowBox[{
       RowBox[{"FirstIntegral", "[", "\[Lambda]", "]"}], "\[Rule]", 
       RowBox[{
        RowBox[{"2", " ", "c", " ", 
         RowBox[{
          SuperscriptBox["r", "\[Prime]",
           MultilineFunction->None], "[", "\[Lambda]", "]"}], " ", 
         RowBox[{
          SuperscriptBox["v", "\[Prime]",
           MultilineFunction->None], "[", "\[Lambda]", "]"}]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "[", 
              RowBox[{"v", "[", "\[Lambda]", "]"}], "]"}]}], 
            RowBox[{"r", "[", "\[Lambda]", "]"}]]}], ")"}], " ", 
         SuperscriptBox[
          RowBox[{
           SuperscriptBox["v", "\[Prime]",
            MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}], "+", 
        RowBox[{
         SuperscriptBox[
          RowBox[{"r", "[", "\[Lambda]", "]"}], "2"], " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox[
            RowBox[{
             SuperscriptBox["\[Theta]", "\[Prime]",
              MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"], "+", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"Sin", "[", 
              RowBox[{"\[Theta]", "[", "\[Lambda]", "]"}], "]"}], "2"], " ", 
            SuperscriptBox[
             RowBox[{
              SuperscriptBox["\[Phi]", "\[Prime]",
               MultilineFunction->None], "[", "\[Lambda]", "]"}], "2"]}]}], 
          ")"}]}]}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.877793562632868*^9, 3.877794014626678*^9, 
  3.877794388519559*^9, 3.877795193219089*^9},
 CellLabel->
  "Out[88]//TableForm=",ExpressionUUID->"d0143f7f-8951-4652-a748-\
7f748930ecd9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "firstIntegralsSimplified", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"firstIntegralsSimplified", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"firstIntegrals", " ", "/.", "  ", 
    RowBox[{
     RowBox[{"q_", "[", "\[Lambda]", "]"}], " ", "\[RuleDelayed]", " ", 
     "q"}]}]}], "  ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"firstIntegralsSimplified", "//", " ", "TableForm", " "}]}], "Input",\

 CellChangeTimes->{{3.8777935768617077`*^9, 3.877793587586488*^9}, {
  3.8777941348641768`*^9, 3.8777941531916237`*^9}},
 CellLabel->"In[89]:=",ExpressionUUID->"37432488-2450-46e1-9e54-299221c831b0"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"FirstIntegral", "[", "\[Phi]", "]"}], "\[Rule]", 
       RowBox[{
        RowBox[{"-", "2"}], " ", 
        SuperscriptBox["r", "2"], " ", 
        SuperscriptBox[
         RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
        SuperscriptBox["\[Phi]", "\[Prime]",
         MultilineFunction->None]}]}]},
     {
      RowBox[{"FirstIntegral", "\[Rule]", 
       RowBox[{
        RowBox[{"2", " ", "c", " ", 
         SuperscriptBox["r", "\[Prime]",
          MultilineFunction->None], " ", 
         SuperscriptBox["v", "\[Prime]",
          MultilineFunction->None]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "[", "v", "]"}]}], "r"]}], ")"}], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           SuperscriptBox["v", "\[Prime]",
            MultilineFunction->None], ")"}], "2"]}], "+", 
        RowBox[{
         SuperscriptBox["r", "2"], " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             SuperscriptBox["\[Theta]", "\[Prime]",
              MultilineFunction->None], ")"}], "2"], "+", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
            SuperscriptBox[
             RowBox[{"(", 
              SuperscriptBox["\[Phi]", "\[Prime]",
               MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{
  3.877793588127228*^9, 3.877794014637744*^9, {3.8777941405892057`*^9, 
   3.87779415374162*^9}, 3.877794388534799*^9, 3.877795193230989*^9},
 CellLabel->
  "Out[91]//TableForm=",ExpressionUUID->"9453185d-c1cd-4989-b398-\
adefb4d882cc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "firstIntegralsConstants", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"firstIntegralsConstants", " ", "=", 
   RowBox[{"{", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"firstIntegralsSimplified", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], " ", "==", " ", "L"}], "  ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"firstIntegralsSimplified", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], " ", "==", "0"}]}], 
    "\[IndentingNewLine]", "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"firstIntegralsConstants", " ", "//", " ", "TableForm"}]}], "Input",
 CellChangeTimes->{{3.8777941595918922`*^9, 3.877794233874661*^9}, {
  3.8777949622204313`*^9, 3.877794962618709*^9}},
 CellLabel->"In[92]:=",ExpressionUUID->"fc5e0c11-ffbe-4a49-ba0d-ae4d0aa031e6"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{
        RowBox[{"-", "2"}], " ", 
        SuperscriptBox["r", "2"], " ", 
        SuperscriptBox[
         RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
        SuperscriptBox["\[Phi]", "\[Prime]",
         MultilineFunction->None]}], "\[Equal]", "L"}]},
     {
      RowBox[{
       RowBox[{
        RowBox[{"2", " ", "c", " ", 
         SuperscriptBox["r", "\[Prime]",
          MultilineFunction->None], " ", 
         SuperscriptBox["v", "\[Prime]",
          MultilineFunction->None]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "[", "v", "]"}]}], "r"]}], ")"}], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           SuperscriptBox["v", "\[Prime]",
            MultilineFunction->None], ")"}], "2"]}], "+", 
        RowBox[{
         SuperscriptBox["r", "2"], " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"(", 
             SuperscriptBox["\[Theta]", "\[Prime]",
              MultilineFunction->None], ")"}], "2"], "+", 
           RowBox[{
            SuperscriptBox[
             RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", 
            SuperscriptBox[
             RowBox[{"(", 
              SuperscriptBox["\[Phi]", "\[Prime]",
               MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}], 
       "\[Equal]", "0"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.8777941602106333`*^9, 3.877794192954871*^9}, 
   3.877794234234598*^9, 3.8777949631298447`*^9, 3.8777951932568617`*^9},
 CellLabel->
  "Out[94]//TableForm=",ExpressionUUID->"d3cae13e-2dc6-4ae6-a9aa-\
e6ff4ef851fd"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "radialGeodesics", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"radialGeodesics", " ", "=", " ", 
   RowBox[{"{", " ", "\[IndentingNewLine]", " ", 
    RowBox[{
     RowBox[{
      SuperscriptBox["\[Theta]", "\[Prime]",
       MultilineFunction->None], "->", " ", "0"}], "  ", ",", 
     "\[IndentingNewLine]", " ", 
     RowBox[{
      SuperscriptBox["\[Phi]", "\[Prime]",
       MultilineFunction->None], "->", " ", "0"}]}], " ", 
    "\[IndentingNewLine]", "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"radialGeodesics", " ", "//", " ", "TableForm"}]}], "Input",
 CellChangeTimes->{{3.877794665609942*^9, 3.877794704692712*^9}},
 CellLabel->"In[95]:=",ExpressionUUID->"4046e5fc-1bfb-4bf8-a3f1-737bd523b1ea"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       SuperscriptBox["\[Theta]", "\[Prime]",
        MultilineFunction->None], "\[Rule]", "0"}]},
     {
      RowBox[{
       SuperscriptBox["\[Phi]", "\[Prime]",
        MultilineFunction->None], "\[Rule]", "0"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.877794705170629*^9, 3.877795193267967*^9},
 CellLabel->
  "Out[97]//TableForm=",ExpressionUUID->"93601ceb-627d-47a0-9f3f-\
ed662b9a3ca2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "geodesicEquationsRadial", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"geodesicEquationsRadial", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
   "geodesicEquationsMetric1Simplified", "  ", "/.", " ", 
    "radialGeodesics"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"geodesicEquationsRadial", " ", "//", " ", "TableForm"}]}], "Input",
 CellChangeTimes->{{3.877794737985854*^9, 3.877794761100829*^9}},
 CellLabel->"In[98]:=",ExpressionUUID->"22ca1141-6634-4711-94c4-9a865c29064e"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       SuperscriptBox["v", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{"-", 
        FractionBox[
         RowBox[{
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         RowBox[{"c", " ", 
          SuperscriptBox["r", "2"]}]]}]}]},
     {
      RowBox[{
       SuperscriptBox["r", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", 
       RowBox[{
        FractionBox[
         RowBox[{"2", " ", 
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox["r", "\[Prime]",
           MultilineFunction->None], " ", 
          SuperscriptBox["v", "\[Prime]",
           MultilineFunction->None]}], 
         RowBox[{"c", " ", 
          SuperscriptBox["r", "2"]}]], "-", 
        FractionBox[
         RowBox[{
          RowBox[{"M", "[", "v", "]"}], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox["r", "2"]}]], "+", 
        FractionBox[
         RowBox[{"2", " ", 
          SuperscriptBox[
           RowBox[{"M", "[", "v", "]"}], "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"]}], 
         RowBox[{
          SuperscriptBox["c", "2"], " ", 
          SuperscriptBox["r", "3"]}]], "-", 
        FractionBox[
         RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
            SuperscriptBox["v", "\[Prime]",
             MultilineFunction->None], ")"}], "2"], " ", 
          RowBox[{
           SuperscriptBox["M", "\[Prime]",
            MultilineFunction->None], "[", "v", "]"}]}], 
         RowBox[{"c", " ", "r"}]]}]}]},
     {
      RowBox[{
       SuperscriptBox["\[Theta]", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", "0"}]},
     {
      RowBox[{
       SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
        MultilineFunction->None], "\[Equal]", "0"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.877794739997122*^9, 3.877794761582438*^9}, 
   3.877795193292769*^9},
 CellLabel->
  "Out[100]//TableForm=",ExpressionUUID->"c23af009-5b36-450f-8d64-\
12e045e8d84c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "firstIntegralsRadial", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"firstIntegralsRadial", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"firstIntegralsConstants", "  ", "/.", " ", "radialGeodesics"}]}], 
  " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"firstIntegralsRadial", "  ", "//", " ", "TableForm"}]}], "Input",
 CellChangeTimes->{{3.877794618490061*^9, 3.877794647434805*^9}, {
  3.877794725379548*^9, 3.877794726768489*^9}, {3.877794764594017*^9, 
  3.8777947656840677`*^9}, {3.8777948390744247`*^9, 3.8777948545542183`*^9}},
 CellLabel->
  "In[101]:=",ExpressionUUID->"80685901-d62d-48f1-a9ff-244234708fb1"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{"0", "\[Equal]", "L"}]},
     {
      RowBox[{
       RowBox[{
        RowBox[{"2", " ", "c", " ", 
         SuperscriptBox["r", "\[Prime]",
          MultilineFunction->None], " ", 
         SuperscriptBox["v", "\[Prime]",
          MultilineFunction->None]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           FractionBox[
            RowBox[{"2", " ", 
             RowBox[{"M", "[", "v", "]"}]}], "r"]}], ")"}], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           SuperscriptBox["v", "\[Prime]",
            MultilineFunction->None], ")"}], "2"]}]}], "\[Equal]", "0"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.877794628301589*^9, 3.8777946478463*^9}, 
   3.877794727257584*^9, 3.8777947660157146`*^9, 3.877794855112361*^9, 
   3.877794975318769*^9, 3.877795193304859*^9},
 CellLabel->
  "Out[103]//TableForm=",ExpressionUUID->"d761b4f6-5010-4167-9294-\
fdffda7890d5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq3", "]"}], "\[IndentingNewLine]", 
 RowBox[{"eq3", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{"geodesicEquationsRadial", "[", 
   RowBox[{"[", "1", "]"}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.8777948138825207`*^9, 3.877794820522419*^9}, 
   3.877794983850768*^9},
 CellLabel->
  "In[104]:=",ExpressionUUID->"939b27ed-7f58-41bc-ab4b-cd3d771eda30"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["v", "\[Prime]\[Prime]",
   MultilineFunction->None], "\[Equal]", 
  RowBox[{"-", 
   FractionBox[
    RowBox[{
     RowBox[{"M", "[", "v", "]"}], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       SuperscriptBox["v", "\[Prime]",
        MultilineFunction->None], ")"}], "2"]}], 
    RowBox[{"c", " ", 
     SuperscriptBox["r", "2"]}]]}]}]], "Output",
 CellChangeTimes->{{3.8777948147107563`*^9, 3.877794821234009*^9}, {
   3.877794982188559*^9, 3.877794984189333*^9}, 3.877795193332251*^9},
 CellLabel->
  "Out[105]=",ExpressionUUID->"457a2f77-65cc-4795-a49e-90c22b77eeac"]
}, Open  ]],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq4", "]"}], "\[IndentingNewLine]", 
 RowBox[{"eq4", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"(", " ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Flatten", "[", 
        RowBox[{"Solve", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"Eliminate", "[", " ", 
            RowBox[{
             RowBox[{"{", " ", 
              RowBox[{
               RowBox[{"geodesicEquationsRadial", "[", 
                RowBox[{"[", "2", "]"}], "]"}], " ", ",", " ", 
               RowBox[{"firstIntegralsRadial", "[", 
                RowBox[{"[", "2", "]"}], "]"}]}], " ", "}"}], ",", 
             SuperscriptBox["r", "\[Prime]",
              MultilineFunction->None]}], "]"}], "[", 
           RowBox[{"[", "1", "]"}], "]"}], ",", " ", 
          SuperscriptBox["r", "\[Prime]\[Prime]",
           MultilineFunction->None]}], "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "Expand"}], " ", "//", 
     " ", "Simplify"}], " ", ")"}], "  ", "/.", " ", 
   RowBox[{"Rule", "->", " ", "Equal", "  "}]}]}]}], "Input",
 CellChangeTimes->{{3.8777948758426723`*^9, 3.877794945069602*^9}, {
  3.877794992189948*^9, 3.877795027739581*^9}},
 CellLabel->
  "In[106]:=",ExpressionUUID->"502f1b1d-fb2a-4eb5-8cba-ba10f52dcf86"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["r", "\[Prime]\[Prime]",
   MultilineFunction->None], "\[Equal]", 
  RowBox[{"-", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       SuperscriptBox["v", "\[Prime]",
        MultilineFunction->None], ")"}], "2"], " ", 
     RowBox[{
      SuperscriptBox["M", "\[Prime]",
       MultilineFunction->None], "[", "v", "]"}]}], 
    RowBox[{"c", " ", "r"}]]}]}]], "Output",
 CellChangeTimes->{{3.877794865716329*^9, 3.877794945393417*^9}, {
   3.877794986918848*^9, 3.8777950284805183`*^9}, 3.877795193360529*^9},
 CellLabel->
  "Out[107]=",ExpressionUUID->"a441d4c8-dbd0-4fa6-a35a-ac94a591e7c2"]
}, Closed]]
},
CellGrouping->Manual,
WindowSize->{1279, 755},
WindowMargins->{{Automatic, 0}, {Automatic, 0}},
FrontEndVersion->"13.0 for Mac OS X x86 (64-bit) (February 4, 2022)",
StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", 
  CharacterEncoding -> "UTF-8"],
ExpressionUUID->"13cbfbe2-276b-4241-9803-a2eb21d71870"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 691, 11, 221, "Title",ExpressionUUID->"5b436d6b-8fd2-4fb6-8187-ad949a029f8c",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[1274, 35, 1402, 23, 94, "Author",ExpressionUUID->"1d2f7d97-d716-4043-9aba-ccc880eadb07",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[2713, 63, 251, 4, 69, "Section",ExpressionUUID->"6a3e8038-bd4a-4bea-9bbb-de286ad7443f",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[CellGroupData[{
Cell[2989, 71, 461, 10, 63, "Input",ExpressionUUID->"d70633e0-19e6-42ef-a9f6-330242d88526",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[3453, 83, 1503, 23, 70, "Output",ExpressionUUID->"df0a06d5-7572-4887-831f-4b2c648166cc",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[5005, 112, 315, 5, 55, "Section",ExpressionUUID->"976370e4-e7b9-45a6-80f4-877ac8b1345e",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[CellGroupData[{
Cell[5345, 121, 1117, 18, 168, "Input",ExpressionUUID->"0c810eb3-9ccb-4111-be8c-43d019b37943",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[6465, 141, 1110, 19, 70, "Output",ExpressionUUID->"a795de3b-ddec-462c-8a73-9036f38bedac",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[7612, 165, 463, 9, 63, "Input",ExpressionUUID->"8b9e3926-43b0-47f1-8a4c-ff6d88a3b258",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[8078, 176, 453, 8, 70, "Output",ExpressionUUID->"38979afc-f31f-4865-a12a-b4467f33cfbf",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[8568, 189, 473, 9, 63, "Input",ExpressionUUID->"1b338a7e-8db4-4038-a521-37c84f78e74b",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[9044, 200, 509, 10, 70, "Output",ExpressionUUID->"30ffb02f-bbe8-4253-98fa-41dba1f8fc99",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[9602, 216, 249, 4, 55, "Section",ExpressionUUID->"a339e41a-05b8-4914-ba69-4e3fb10cf2dd",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[CellGroupData[{
Cell[9876, 224, 1634, 43, 210, "Input",ExpressionUUID->"0585550f-429a-4a87-b246-6709ff80272b",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[11513, 269, 706, 14, 70, "Print",ExpressionUUID->"a316e061-383b-4adf-a0e6-fd3f8b2a60f5",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[12222, 285, 721, 15, 70, "Print",ExpressionUUID->"1685a00d-5891-473f-becf-15faea27d9db",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[12946, 302, 705, 12, 70, "Output",ExpressionUUID->"d9dfcbd4-f84d-4c7b-8349-3a5698b1bdfe",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[13666, 317, 266, 4, 41, "Input",ExpressionUUID->"a604b8e4-786c-46f3-9ff1-2245f97702e1",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[13935, 323, 259, 4, 41, "Input",ExpressionUUID->"22cbcd6e-fa88-48b6-b605-1018783c8ae3",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Closed]],
Cell[CellGroupData[{
Cell[14231, 332, 265, 5, 55, "Section",ExpressionUUID->"48720785-4b5b-421c-b4a7-11424800c40b",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[CellGroupData[{
Cell[14521, 341, 4473, 101, 714, "Input",ExpressionUUID->"6ecb8f3a-2655-4f35-8e81-9352fb4f1255",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[18997, 444, 3590, 112, 70, "Output",ExpressionUUID->"928b6808-4e3e-4da2-9962-f75c85807489",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Open  ]],
Cell[22602, 559, 902, 22, 84, "Input",ExpressionUUID->"28c33fed-7c50-44a6-ac4f-868f681b2295",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Closed]],
Cell[CellGroupData[{
Cell[23541, 586, 362, 6, 55, "Section",ExpressionUUID->"e99f309f-36a0-4b66-9d82-288bda8e9e0c",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}],
Cell[23906, 594, 1660, 41, 126, "Input",ExpressionUUID->"7f389239-c788-4969-b90f-baa732652cfa",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}],
Cell[25569, 637, 1056, 26, 84, "Input",ExpressionUUID->"91dc6abe-f4e8-4b33-b634-1222a2b717c8",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}]
}, Closed]],
Cell[CellGroupData[{
Cell[26662, 668, 435, 7, 55, "Section",ExpressionUUID->"9b34d0ec-434b-4cfb-9647-3a6262596bf0",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[CellGroupData[{
Cell[27122, 679, 1579, 38, 144, "Input",ExpressionUUID->"cb79e021-1f9f-4aab-8404-ef4cb5690f5e",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[28704, 719, 912, 24, 70, "Output",ExpressionUUID->"44849638-0d9b-477e-82ea-c2fc6a4239f5",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[29653, 748, 851, 17, 105, "Input",ExpressionUUID->"382092ec-474a-41c8-859d-d594c89b724f",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[30507, 767, 1318, 35, 70, "Output",ExpressionUUID->"a8838432-3444-4c09-aca6-3e8c1a0f577a",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[31874, 808, 462, 7, 55, "Section",ExpressionUUID->"60651d99-915e-4e91-8c55-5bc06d1bdf5b",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[32339, 817, 5470, 126, 714, "Input",ExpressionUUID->"7801844e-a52e-4fa7-855b-8e105e0b75b3",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[CellGroupData[{
Cell[37834, 947, 934, 19, 65, "Input",ExpressionUUID->"41cdc62c-941d-4b74-9e22-e6b437da84d8",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[38771, 968, 470, 8, 70, "Output",ExpressionUUID->"c36bbda2-0fd9-4977-9d80-e5598dd2c725",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[39278, 981, 655, 15, 84, "Input",ExpressionUUID->"1fddb260-c82f-45e2-a39d-9ac2617be5ce",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[39936, 998, 568, 11, 70, "Output",ExpressionUUID->"09fc6cea-2680-4add-9cee-21df7652c6d2",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[40507, 1011, 480, 7, 70, "Output",ExpressionUUID->"620032f6-a8f3-4e85-969a-d5b19d6ccedb",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[40990, 1020, 1347, 36, 70, "Output",ExpressionUUID->"cf1f162f-9f1f-4606-809d-e10ea51e15a7",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[42374, 1061, 654, 15, 84, "Input",ExpressionUUID->"6b4655ff-4f3e-496d-acc3-66a5dd9595bc",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[43031, 1078, 577, 11, 70, "Output",ExpressionUUID->"f3c0c657-7e9d-4631-afbb-b16fe36ae7e1",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[43611, 1091, 473, 6, 70, "Output",ExpressionUUID->"2224f594-4256-4a90-9791-fbd67368700b",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[44087, 1099, 12200, 363, 70, "Output",ExpressionUUID->"d5b91e4a-c207-47ee-a43c-4f1faca4372a",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[56324, 1467, 655, 15, 84, "Input",ExpressionUUID->"3e3b2052-7f5e-446f-aae0-14accd33de8e",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[56982, 1484, 529, 9, 70, "Output",ExpressionUUID->"73c5c715-f298-477d-8bac-35027341b59d",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[57514, 1495, 471, 6, 70, "Output",ExpressionUUID->"ed2ee329-194c-4b3c-a1e4-a27945c80c62",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[57988, 1503, 21130, 562, 70, "Output",ExpressionUUID->"95c47167-2925-469f-8168-acfad889ac08",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[79155, 2070, 657, 15, 84, "Input",ExpressionUUID->"1deed3bd-db51-4e7c-a588-c98ddce75e11",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[79815, 2087, 515, 9, 70, "Output",ExpressionUUID->"8ce388ec-4854-47a1-9ced-5e7e8d9b0a11",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[80333, 2098, 466, 6, 70, "Output",ExpressionUUID->"6f8082c7-c07c-4f24-ba39-f23518409649",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[80802, 2106, 1665, 46, 70, "Output",ExpressionUUID->"b07d1831-2772-4371-a40b-f4354d9b2aaf",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[82504, 2157, 657, 15, 84, "Input",ExpressionUUID->"ae0ff631-5b58-486d-aa44-2a6431db8377",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[83164, 2174, 464, 8, 70, "Output",ExpressionUUID->"7415f0a1-243c-4a5f-ad09-1f051ac6d15e",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[83631, 2184, 452, 6, 70, "Output",ExpressionUUID->"a17f5783-6dbc-4278-a278-d97b4fea073c",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[84086, 2192, 754, 20, 70, "Output",ExpressionUUID->"1c403127-496d-4227-8032-3feb4829c97a",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[84877, 2217, 656, 15, 84, "Input",ExpressionUUID->"73f96c28-b8c2-494a-97a3-868a96b91db6",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[85536, 2234, 469, 8, 70, "Output",ExpressionUUID->"864e4815-ccce-4a7e-9da5-9bc984194fd6",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[86008, 2244, 466, 6, 70, "Output",ExpressionUUID->"317f48ee-208c-4f3f-aa21-d1df28a7ed4f",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[86477, 2252, 1191, 33, 70, "Output",ExpressionUUID->"2a26cfee-e39d-4599-b150-615681a59737",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[87705, 2290, 655, 15, 84, "Input",ExpressionUUID->"b996a705-b105-4f36-a838-ebcbd2d69028",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[88363, 2307, 509, 9, 70, "Output",ExpressionUUID->"98310f91-ca83-4f95-bf2d-cec5f43f0a75",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[88875, 2318, 468, 6, 70, "Output",ExpressionUUID->"adf18f83-d26a-485f-9fdc-3bf36095e917",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[89346, 2326, 2017, 56, 70, "Output",ExpressionUUID->"9d87ee65-7619-4f7a-9624-20da664b0726",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[91400, 2387, 659, 15, 84, "Input",ExpressionUUID->"ae7ca38a-25ce-4411-8113-58e7489f028a",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[92062, 2404, 523, 9, 70, "Output",ExpressionUUID->"9293acdf-6420-4243-8391-f3c2e03798f3",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[92588, 2415, 462, 6, 70, "Output",ExpressionUUID->"c67ec192-4982-4e57-91c6-d74301731bf5",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[93053, 2423, 25451, 690, 70, "Output",ExpressionUUID->"b1107e3d-5677-444b-99f5-8d0b55455e37",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[118541, 3118, 657, 15, 84, "Input",ExpressionUUID->"89764af5-ff84-49a4-b275-ad5811bc5eae",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[119201, 3135, 521, 9, 70, "Output",ExpressionUUID->"5b6d9312-1981-4115-bfe6-93e9e38e457a",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[119725, 3146, 466, 6, 70, "Output",ExpressionUUID->"8e8e5841-d1ff-4db5-b186-9b54308a90a1",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[120194, 3154, 14693, 425, 70, "Output",ExpressionUUID->"f5d13578-d8ff-468f-96b5-183d55274dc1",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[134936, 3585, 354, 5, 55, "Section",ExpressionUUID->"c188ac9d-8f87-451c-8e6b-4138386107c2",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[CellGroupData[{
Cell[135315, 3594, 1448, 33, 105, "Input",ExpressionUUID->"c9e8bd40-a47c-4e4c-86d6-aadcbf669410",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[136766, 3629, 1353, 43, 70, "Output",ExpressionUUID->"56f5e224-1d86-4a4b-b4f0-146b13add967",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[138156, 3677, 1475, 36, 105, "Input",ExpressionUUID->"38aa22b9-9624-403f-8545-c4c6f4ac9a68",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[139634, 3715, 1626, 48, 70, "Output",ExpressionUUID->"03fd4318-860b-453d-af42-e21de6ce7954",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[141309, 3769, 374, 6, 55, "Section",ExpressionUUID->"24a5e37c-8886-4ee6-a108-08e6ba91ba59",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[141686, 3777, 4855, 107, 552, "Input",ExpressionUUID->"9be93aa5-d7d4-4bc4-8819-1b1010270f8e",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[146544, 3886, 809, 16, 147, "Input",ExpressionUUID->"5a8a932e-228b-4f7f-8a53-19e35bea8d83",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[CellGroupData[{
Cell[147378, 3906, 738, 16, 105, "Input",ExpressionUUID->"a1707b9d-b200-4115-98fb-7f1c9ff75d11"],
Cell[148119, 3924, 7600, 203, 159, "Output",ExpressionUUID->"508074b0-9cb0-4559-aa59-7944efe07379"]
}, Open  ]],
Cell[CellGroupData[{
Cell[155756, 4132, 746, 15, 105, "Input",ExpressionUUID->"f267e8fc-024c-4eda-b315-1d8b81c38de1"],
Cell[156505, 4149, 5868, 165, 153, "Output",ExpressionUUID->"d850120c-3b1e-4ed3-8c4b-0e139ede8e47"]
}, Open  ]],
Cell[CellGroupData[{
Cell[162410, 4319, 491, 9, 105, "Input",ExpressionUUID->"db7becd4-1e02-4026-b6c0-9ced2044d356"],
Cell[162904, 4330, 2675, 74, 81, "Output",ExpressionUUID->"d0143f7f-8951-4652-a748-7f748930ecd9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[165616, 4409, 648, 13, 105, "Input",ExpressionUUID->"37432488-2450-46e1-9e54-299221c831b0"],
Cell[166267, 4424, 2228, 64, 81, "Output",ExpressionUUID->"9453185d-c1cd-4989-b398-adefb4d882cc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[168532, 4493, 978, 22, 147, "Input",ExpressionUUID->"fc5e0c11-ffbe-4a49-ba0d-ae4d0aa031e6"],
Cell[169513, 4517, 2156, 63, 81, "Output",ExpressionUUID->"d3cae13e-2dc6-4ae6-a9aa-e6ff4ef851fd"]
}, Open  ]],
Cell[CellGroupData[{
Cell[171706, 4585, 764, 16, 147, "Input",ExpressionUUID->"4046e5fc-1bfb-4bf8-a3f1-737bd523b1ea"],
Cell[172473, 4603, 830, 26, 69, "Output",ExpressionUUID->"93601ceb-627d-47a0-9f3f-ed662b9a3ca2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[173340, 4634, 536, 10, 105, "Input",ExpressionUUID->"22ca1141-6634-4711-94c4-9a865c29064e"],
Cell[173879, 4646, 2863, 86, 135, "Output",ExpressionUUID->"c23af009-5b36-450f-8d64-12e045e8d84c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[176779, 4737, 667, 11, 105, "Input",ExpressionUUID->"80685901-d62d-48f1-a9ff-244234708fb1"],
Cell[177449, 4750, 1384, 41, 77, "Output",ExpressionUUID->"d761b4f6-5010-4167-9294-fdffda7890d5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[178870, 4796, 398, 8, 84, "Input",ExpressionUUID->"939b27ed-7f58-41bc-ab4b-cd3d771eda30"],
Cell[179271, 4806, 618, 17, 62, "Output",ExpressionUUID->"457a2f77-65cc-4795-a49e-90c22b77eeac"]
}, Open  ]],
Cell[179904, 4826, 1323, 31, 84, "Input",ExpressionUUID->"502f1b1d-fb2a-4eb5-8cba-ba10f52dcf86"],
Cell[181230, 4859, 658, 18, 60, "Output",ExpressionUUID->"a441d4c8-dbd0-4fa6-a35a-ac94a591e7c2"]
}, Closed]]
}
]
*)