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Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`METRIC$$ = "min", $CellContext`phi$$ = 
    0., $CellContext`rad$$ = 6., $CellContext`sim$$ = 
    "2D", $CellContext`simtime$$ = 100, $CellContext`spin$$ = 
    1., $CellContext`theta$$ = Rational[1, 2] 
    Pi, $CellContext`udotu$$ = -1, $CellContext`uphi$$ = 
    0.09622504486493762, $CellContext`urad$$ = 0, $CellContext`utheta$$ = 0, 
    Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`udotu$$], -1, ""}, {-1 -> "Massive Particle", 0 -> 
       "Photon"}}, {{
       Hold[$CellContext`sim$$], "2D", "Dim"}, {"2D", "3D"}}, {{
       Hold[$CellContext`simtime$$], 100, 
       "\!\(\*SubscriptBox[\(T\), \(sim\)]\)"}, 10, 5000, 50}, {{
       Hold[$CellContext`spin$$], 1., "Spin"}, 0., 5.}, {{
       Hold[$CellContext`METRIC$$], "sch", "Metric"}, {
      "sch" -> "Schwarzschild", "kerr" -> "Kerr", "min" -> "Minkowski"}}, {{
       Hold[$CellContext`rad$$], 6., "r"}, 2.1, 20., 1.}, {{
       Hold[$CellContext`phi$$], 0., "\[Phi]"}, 0., 2 Pi, 0.1}, {{
       Hold[$CellContext`theta$$], Rational[1, 2] Pi, "\[Theta]"}, 0., Pi, 
      0.1}, {{
       Hold[$CellContext`urad$$], 0, 
       "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"}, -1., 1., 0.1}, {{
       Hold[$CellContext`uphi$$], 0.09622504486493762, 
       "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"}, -1., 1., 0.1}, {{
       Hold[$CellContext`utheta$$], 0, 
       "\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"}, -1., 1., 0.1}}, 
    Typeset`size$$ = {606., {410., 420.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`udotu$1222$$ = False, $CellContext`sim$1223$$ = 
    False, $CellContext`simtime$1224$$ = 0, $CellContext`spin$1225$$ = 
    0, $CellContext`METRIC$1226$$ = False, $CellContext`rad$1227$$ = 
    0, $CellContext`phi$1228$$ = 0, $CellContext`theta$1229$$ = 
    0, $CellContext`urad$1230$$ = 0, $CellContext`uphi$1231$$ = 
    0, $CellContext`utheta$1232$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`METRIC$$ = "sch", $CellContext`phi$$ = 
        0., $CellContext`rad$$ = 6., $CellContext`sim$$ = 
        "2D", $CellContext`simtime$$ = 100, $CellContext`spin$$ = 
        1., $CellContext`theta$$ = 
        Rational[1, 2] Pi, $CellContext`udotu$$ = -1, $CellContext`uphi$$ = 
        0.09622504486493762, $CellContext`urad$$ = 0, $CellContext`utheta$$ = 
        0}, "ControllerVariables" :> {
        Hold[$CellContext`udotu$$, $CellContext`udotu$1222$$, False], 
        Hold[$CellContext`sim$$, $CellContext`sim$1223$$, False], 
        Hold[$CellContext`simtime$$, $CellContext`simtime$1224$$, 0], 
        Hold[$CellContext`spin$$, $CellContext`spin$1225$$, 0], 
        Hold[$CellContext`METRIC$$, $CellContext`METRIC$1226$$, False], 
        Hold[$CellContext`rad$$, $CellContext`rad$1227$$, 0], 
        Hold[$CellContext`phi$$, $CellContext`phi$1228$$, 0], 
        Hold[$CellContext`theta$$, $CellContext`theta$1229$$, 0], 
        Hold[$CellContext`urad$$, $CellContext`urad$1230$$, 0], 
        Hold[$CellContext`uphi$$, $CellContext`uphi$1231$$, 0], 
        Hold[$CellContext`utheta$$, $CellContext`utheta$1232$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> 
      Module[{$CellContext`soln$, $CellContext`metric$, \
$CellContext`geodesic$, $CellContext`cartsoln$, $CellContext`mass$ = 1.}, 
        Which[$CellContext`METRIC$$ == 
          "sch", $CellContext`metric$ = \
$CellContext`schwarz[$CellContext`mass$]; $CellContext`geodesic$ = \
$CellContext`geodesic\[LetterSpace]sch[$CellContext`mass$], \
$CellContext`METRIC$$ == 
          "kerr", $CellContext`metric$ = \
$CellContext`kerr[$CellContext`mass$, $CellContext`spin$$]; \
$CellContext`geodesic$ = \
$CellContext`geodesic\[LetterSpace]kerr[$CellContext`mass$, \
$CellContext`spin$$], $CellContext`METRIC$$ == 
          "min", $CellContext`metric$ = $CellContext`minkowski[]; \
$CellContext`geodesic$ = $CellContext`findgeodesic[$CellContext`metric$]]; \
$CellContext`soln$ = $CellContext`trajectory[{
           0, $CellContext`rad$$, $CellContext`theta$$, $CellContext`phi$$}, \
{$CellContext`urad$$, $CellContext`utheta$$, $CellContext`uphi$$}, \
$CellContext`udotu$$, $CellContext`mass$, $CellContext`simtime$$, \
$CellContext`metric$, $CellContext`geodesic$]; $CellContext`cartsoln$ = \
$CellContext`sphslnToCartsln[$CellContext`soln$]; \
$CellContext`animator[$CellContext`soln$, $CellContext`cartsoln$, \
$CellContext`sim$$]], 
      "Specifications" :> {{{$CellContext`udotu$$, -1, ""}, {-1 -> 
          "Massive Particle", 0 -> "Photon"}, ControlType -> 
         RadioButton}, {{$CellContext`sim$$, "2D", "Dim"}, {"2D", "3D"}, 
         ControlType -> 
         RadioButton}, {{$CellContext`simtime$$, 100, 
          "\!\(\*SubscriptBox[\(T\), \(sim\)]\)"}, 10, 5000, 50, Appearance -> 
         "Labeled"}, 
        Delimiter, {{$CellContext`spin$$, 1., "Spin"}, 0., 5., Appearance -> 
         "Labeled"}, {{$CellContext`METRIC$$, "sch", "Metric"}, {
         "sch" -> "Schwarzschild", "kerr" -> "Kerr", "min" -> "Minkowski"}, 
         ControlType -> PopupMenu}, 
        Delimiter, {{$CellContext`rad$$, 6., "r"}, 2.1, 20., 1., Appearance -> 
         "Labeled"}, {{$CellContext`phi$$, 0., "\[Phi]"}, 0., 2 Pi, 0.1, 
         Appearance -> 
         "Labeled"}, {{$CellContext`theta$$, Rational[1, 2] Pi, "\[Theta]"}, 
         0., Pi, 0.1, Appearance -> "Labeled"}, 
        Delimiter, {{$CellContext`urad$$, 0, 
          "\!\(\*SuperscriptBox[\(u\), \(r\)]\)"}, -1., 1., 0.1, Appearance -> 
         "Labeled"}, {{$CellContext`uphi$$, 0.09622504486493762, 
          "\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)"}, -1., 1., 0.1, 
         Appearance -> 
         "Labeled"}, {{$CellContext`utheta$$, 0, 
          "\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"}, -1., 1., 0.1, 
         Appearance -> "Labeled"}}, "Options" :> {ControlPlacement -> Left}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{1289., {459., 469.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`schwarz[
         Pattern[$CellContext`mass\[LetterSpace]sch, 
          Blank[]]] := 
       Module[{$CellContext`M = $CellContext`mass\[LetterSpace]sch, \
$CellContext`g}, $CellContext`g = {{-1 + (2 $CellContext`M)/$CellContext`r, 0,
             0, 0}, {
           0, $CellContext`r^2/((-2) $CellContext`M $CellContext`r + \
$CellContext`r^2), 0, 0}, {0, 0, $CellContext`r^2, 0}, {
           0, 0, 0, $CellContext`r^2 
            Sin[$CellContext`\[Theta]]^2}}], $CellContext`geodesic\
\[LetterSpace]sch[
         Pattern[$CellContext`mass\[LetterSpace]sch$, 
          Blank[]]] := 
       ReplaceAll[$CellContext`rhs$1167, {$CellContext`M$1167 :> \
$CellContext`mass\[LetterSpace]sch$}], 
       Attributes[$CellContext`mass\[LetterSpace]sch$] = {Temporary}, 
       Attributes[$CellContext`rhs$1167] = {
        Temporary}, $CellContext`rhs$1167 = {(2 $CellContext`M$1167 
          Derivative[1][$CellContext`r] Derivative[1][$CellContext`t])/(
         2 $CellContext`M$1167 $CellContext`r - $CellContext`r^2), \
(-($CellContext`M$1167 $CellContext`r^2 
            Derivative[
              1][$CellContext`r]^2) + ((-2) $CellContext`M$1167 + \
$CellContext`r)^2 ($CellContext`M$1167 
             Derivative[1][$CellContext`t]^2 - $CellContext`r^3 (
             Derivative[1][$CellContext`\[Theta]]^2 + 
             Sin[$CellContext`\[Theta]]^2 
              Derivative[1][$CellContext`\[Phi]]^2)))/((
          2 $CellContext`M$1167 - $CellContext`r) $CellContext`r^3), ((-2) 
           Derivative[1][$CellContext`r] 
           Derivative[1][$CellContext`\[Theta]])/$CellContext`r + 
         Cos[$CellContext`\[Theta]] Sin[$CellContext`\[Theta]] 
          Derivative[1][$CellContext`\[Phi]]^2, ((-2) (
           Derivative[1][$CellContext`r] + $CellContext`r 
            Cot[$CellContext`\[Theta]] Derivative[1][$CellContext`\[Theta]]) 
          Derivative[1][$CellContext`\[Phi]])/$CellContext`r}, 
       Attributes[$CellContext`M$1167] = {Temporary}, 
       Attributes[Derivative] = {NHoldAll, ReadProtected}, $CellContext`kerr[
         Pattern[$CellContext`mass\[LetterSpace]sch, 
          Blank[]], 
         Pattern[$CellContext`spin\[LetterSpace]kerr, 
          Blank[]]] := 
       Module[{$CellContext`M = $CellContext`mass\[LetterSpace]sch, \
$CellContext`a = $CellContext`spin\[LetterSpace]kerr, $CellContext`g, \
$CellContext`tt, $CellContext`rr, $CellContext`\[Theta]\[Theta], \
$CellContext`\[Phi]\[Phi], $CellContext`t\[Phi], $CellContext`\[Rho], \
$CellContext`\[CapitalDelta]}, $CellContext`tt = -(1 - 
            2 $CellContext`M ($CellContext`r/$CellContext`\[Rho])); \
$CellContext`rr = $CellContext`\[Rho]/$CellContext`\[CapitalDelta]; \
$CellContext`\[Theta]\[Theta] = $CellContext`\[Rho]; \
$CellContext`\[Phi]\[Phi] = ($CellContext`\[CapitalDelta] + (
              2 $CellContext`M $CellContext`r ($CellContext`r^2 + \
$CellContext`a^2))/$CellContext`\[Rho]) 
           Sin[$CellContext`\[Theta]]^2; $CellContext`t\[Phi] = (-4) \
$CellContext`a $CellContext`M $CellContext`r (
            Sin[$CellContext`\[Theta]]^2/$CellContext`\[Rho]); $CellContext`\
\[Rho] = $CellContext`r^2 + $CellContext`a^2 
            Cos[$CellContext`\[Theta]]^2; $CellContext`\[CapitalDelta] = \
$CellContext`r^2 - 
           2 $CellContext`M $CellContext`r + $CellContext`a^2; $CellContext`g = \
{{$CellContext`tt, 0, 0, $CellContext`t\[Phi]}, {0, $CellContext`rr, 0, 0}, {
            0, 0, $CellContext`\[Theta]\[Theta], 0}, {$CellContext`t\[Phi], 0,
              0, $CellContext`\[Phi]\[Phi]}}], $CellContext`geodesic\
\[LetterSpace]kerr[
         Pattern[$CellContext`mass\[LetterSpace]kerr$, 
          Blank[]], 
         Pattern[$CellContext`spin\[LetterSpace]kerr$, 
          Blank[]]] := 
       ReplaceAll[$CellContext`rhs$1160, {$CellContext`M$1160 :> \
$CellContext`mass\[LetterSpace]kerr$, $CellContext`a$1160 :> \
$CellContext`spin\[LetterSpace]kerr$}], 
       Attributes[$CellContext`mass\[LetterSpace]kerr$] = {Temporary}, 
       Attributes[$CellContext`spin\[LetterSpace]kerr$] = {Temporary}, 
       Attributes[$CellContext`rhs$1160] = {
        Temporary}, $CellContext`rhs$1160 = {($CellContext`M$1160 \
($CellContext`a$1160^2 $CellContext`r 
            Derivative[1][$CellContext`\[Theta]] (
             2 ($CellContext`a$1160^4 + 
               2 $CellContext`r^3 ((-8) $CellContext`M$1160 + $CellContext`r) + \
$CellContext`a$1160^2 $CellContext`r ((-14) $CellContext`M$1160 + 
                 3 $CellContext`r) + $CellContext`a$1160^2 \
($CellContext`a$1160^2 + $CellContext`r ((-2) $CellContext`M$1160 + \
$CellContext`r)) Cos[2 $CellContext`\[Theta]]) Sin[2 $CellContext`\[Theta]] 
              Derivative[1][$CellContext`t] - 
             8 $CellContext`a$1160 ($CellContext`a$1160^2 + $CellContext`r \
((-2) $CellContext`M$1160 + $CellContext`r)) 
             Cos[$CellContext`\[Theta]] ($CellContext`a$1160^2 + 
              2 $CellContext`r^2 + $CellContext`a$1160^2 
               Cos[2 $CellContext`\[Theta]]) Sin[$CellContext`\[Theta]]^3 
             Derivative[1][$CellContext`\[Phi]]) + 
           Derivative[
             1][$CellContext`r] (($CellContext`a$1160^2 - 
               2 $CellContext`r^2 + $CellContext`a$1160^2 
                Cos[2 $CellContext`\[Theta]]) ($CellContext`a$1160^4 + 
               2 $CellContext`r^4 + 
               3 $CellContext`a$1160^2 $CellContext`r ((-2) \
$CellContext`M$1160 + $CellContext`r) + $CellContext`a$1160^2 \
($CellContext`a$1160^2 + $CellContext`r (
                   6 $CellContext`M$1160 + $CellContext`r)) 
                Cos[2 $CellContext`\[Theta]]) Derivative[1][$CellContext`t] + 
             8 $CellContext`a$1160 (($CellContext`r^4 ($CellContext`a$1160^2 + 
                   3 $CellContext`r^2) + (-$CellContext`a$1160^6 + \
$CellContext`a$1160^4 $CellContext`r^2) Cos[$CellContext`\[Theta]]^4) 
                Sin[$CellContext`\[Theta]]^2 + $CellContext`a$1160^2 \
$CellContext`r^4 Sin[2 $CellContext`\[Theta]]^2) 
              Derivative[1][$CellContext`\[Phi]])))/(
         2 ($CellContext`r^2 + $CellContext`a$1160^2 
           Cos[$CellContext`\[Theta]]^2) (
          2 $CellContext`a$1160^2 $CellContext`r^2 ($CellContext`a$1160^2 + 
            2 $CellContext`M$1160^2 - 
            2 $CellContext`M$1160 $CellContext`r + $CellContext`r^2) 
           Cos[$CellContext`\[Theta]]^2 + $CellContext`a$1160^4 \
($CellContext`a$1160^2 + $CellContext`r ((-2) $CellContext`M$1160 + \
$CellContext`r)) 
           Cos[$CellContext`\[Theta]]^4 + $CellContext`r^2 ($CellContext`r^3 \
((-2) $CellContext`M$1160 + $CellContext`r) + $CellContext`a$1160^2 (
              4 $CellContext`M$1160^2 + $CellContext`r^2) - 
            8 $CellContext`a$1160^2 $CellContext`M$1160^2 
            Cos[2 $CellContext`\[Theta]]))), (-((($CellContext`r^2 + \
$CellContext`a$1160^2 
                Cos[$CellContext`\[Theta]]^2)^2 ($CellContext`r \
($CellContext`a$1160^2 - $CellContext`M$1160 $CellContext`r) + \
$CellContext`a$1160^2 ($CellContext`M$1160 - $CellContext`r) 
               Cos[$CellContext`\[Theta]]^2) 
             Derivative[
               1][$CellContext`r]^2)/($CellContext`a$1160^2 + $CellContext`r \
((-2) $CellContext`M$1160 + $CellContext`r))) + $CellContext`M$1160 \
($CellContext`a$1160^2 + $CellContext`r ((-2) $CellContext`M$1160 + \
$CellContext`r)) (-$CellContext`r^2 + $CellContext`a$1160^2 
             Cos[$CellContext`\[Theta]]^2) Derivative[1][$CellContext`t]^2 + 
          2 $CellContext`a$1160^2 
           Cos[$CellContext`\[Theta]] ($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2 
           Sin[$CellContext`\[Theta]] Derivative[1][$CellContext`r] 
           Derivative[
            1][$CellContext`\[Theta]] + $CellContext`r ($CellContext`a$1160^2 + \
$CellContext`r ((-2) $CellContext`M$1160 + $CellContext`r)) ($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2 
           Derivative[1][$CellContext`\[Theta]]^2 - 
          4 $CellContext`a$1160 $CellContext`M$1160 ($CellContext`a$1160^2 + \
$CellContext`r ((-2) $CellContext`M$1160 + $CellContext`r)) \
(-$CellContext`r^2 + $CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2) 
          Sin[$CellContext`\[Theta]]^2 Derivative[1][$CellContext`t] 
          Derivative[
           1][$CellContext`\[Phi]] - ($CellContext`a$1160^2 + $CellContext`r \
((-2) $CellContext`M$1160 + $CellContext`r)) ($CellContext`a$1160^2 \
$CellContext`M$1160 $CellContext`r^2 - $CellContext`r^5 - \
$CellContext`a$1160^2 ($CellContext`a$1160^2 $CellContext`M$1160 + \
$CellContext`r^2 ($CellContext`M$1160 + 2 $CellContext`r)) 
           Cos[$CellContext`\[Theta]]^2 + $CellContext`a$1160^4 \
($CellContext`M$1160 - $CellContext`r) Cos[$CellContext`\[Theta]]^4) 
          Sin[$CellContext`\[Theta]]^2 
          Derivative[
            1][$CellContext`\[Phi]]^2)/($CellContext`r^2 + \
$CellContext`a$1160^2 
           Cos[$CellContext`\[Theta]]^2)^3, (-(($CellContext`a$1160^2 
             Cos[$CellContext`\[Theta]] ($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2 
             Sin[$CellContext`\[Theta]] 
             Derivative[
               1][$CellContext`r]^2)/($CellContext`a$1160^2 + $CellContext`r \
((-2) $CellContext`M$1160 + $CellContext`r))) + $CellContext`a$1160^2 \
$CellContext`M$1160 $CellContext`r Sin[2 $CellContext`\[Theta]] 
           Derivative[1][$CellContext`t]^2 - 
          2 $CellContext`r ($CellContext`r^2 + $CellContext`a$1160^2 
             Cos[$CellContext`\[Theta]]^2)^2 Derivative[1][$CellContext`r] 
          Derivative[1][$CellContext`\[Theta]] + $CellContext`a$1160^2 
           Cos[$CellContext`\[Theta]] ($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2 
           Sin[$CellContext`\[Theta]] Derivative[1][$CellContext`\[Theta]]^2 - 
          4 $CellContext`a$1160 $CellContext`M$1160 $CellContext`r \
($CellContext`a$1160^2 + $CellContext`r^2) Sin[2 $CellContext`\[Theta]] 
          Derivative[1][$CellContext`t] Derivative[1][$CellContext`\[Phi]] + 
          Cos[$CellContext`\[Theta]] ($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2 
           Sin[$CellContext`\[Theta]] ($CellContext`a$1160^2 - 
            2 $CellContext`M$1160 $CellContext`r + $CellContext`r^2 + (
              2 $CellContext`M$1160 $CellContext`r ($CellContext`a$1160^2 + \
$CellContext`r^2))/($CellContext`r^2 + $CellContext`a$1160^2 
              Cos[$CellContext`\[Theta]]^2) + (
              2 $CellContext`a$1160^2 $CellContext`M$1160 $CellContext`r \
($CellContext`a$1160^2 + $CellContext`r^2) 
              Sin[$CellContext`\[Theta]]^2)/($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^2) 
           Derivative[
             1][$CellContext`\[Phi]]^2)/($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2)^3, ((-2) (
           Derivative[
             1][$CellContext`\[Theta]] ((-2) $CellContext`a$1160 \
$CellContext`M$1160 $CellContext`r ($CellContext`a$1160^2 + $CellContext`r \
((-2) $CellContext`M$1160 + $CellContext`r)) ($CellContext`a$1160^2 + 
               2 $CellContext`r^2 + $CellContext`a$1160^2 
                Cos[2 $CellContext`\[Theta]]) Cot[$CellContext`\[Theta]] 
              Derivative[
               1][$CellContext`t] + (($CellContext`a$1160^2 $CellContext`r^2 \
($CellContext`a$1160^2 ((-4) $CellContext`M$1160^2 + 
                    3 $CellContext`r^2) + $CellContext`r^2 (
                    4 $CellContext`M$1160^2 - 
                    6 $CellContext`M$1160 $CellContext`r + 
                    3 $CellContext`r^2)) 
                  Cos[$CellContext`\[Theta]]^2 + $CellContext`a$1160^4 \
$CellContext`r^2 (3 $CellContext`a$1160^2 + 4 $CellContext`M$1160^2 - 
                   6 $CellContext`M$1160 $CellContext`r + 3 $CellContext`r^2) 
                  Cos[$CellContext`\[Theta]]^4 + $CellContext`a$1160^6 \
($CellContext`a$1160^2 + $CellContext`r ((-2) $CellContext`M$1160 + \
$CellContext`r)) 
                  Cos[$CellContext`\[Theta]]^6 + $CellContext`r^2 \
($CellContext`r^5 ((-2) $CellContext`M$1160 + $CellContext`r) + \
$CellContext`a$1160^4 $CellContext`M$1160 (
                    6 $CellContext`M$1160 + $CellContext`r) + \
$CellContext`a$1160^2 $CellContext`r^2 (
                    2 $CellContext`M$1160^2 + $CellContext`M$1160 \
$CellContext`r + $CellContext`r^2) - $CellContext`a$1160^2 \
$CellContext`M$1160 (
                    6 $CellContext`M$1160 + $CellContext`r) \
($CellContext`a$1160^2 + $CellContext`r^2) Cos[2 $CellContext`\[Theta]])) 
                Cot[$CellContext`\[Theta]] + 
               2 $CellContext`a$1160^4 $CellContext`M$1160 $CellContext`r \
($CellContext`a$1160^2 + $CellContext`r^2) Cos[$CellContext`\[Theta]]^3 
                Sin[$CellContext`\[Theta]]) 
              Derivative[1][$CellContext`\[Phi]]) + 
           Derivative[1][$CellContext`r] (
             2 $CellContext`a$1160 $CellContext`M$1160 ($CellContext`r^4 - \
$CellContext`a$1160^4 Cos[$CellContext`\[Theta]]^4) 
              Derivative[1][$CellContext`t] + (
               2 $CellContext`a$1160^2 $CellContext`M$1160^2 $CellContext`r^3 - \
$CellContext`a$1160^2 $CellContext`M$1160 $CellContext`r^4 - 
               2 $CellContext`M$1160 $CellContext`r^6 + $CellContext`r^7 - \
$CellContext`a$1160^2 $CellContext`r (
                2 $CellContext`a$1160^2 $CellContext`M$1160^2 + 
                2 $CellContext`M$1160^2 $CellContext`r^2 + 
                3 $CellContext`M$1160 $CellContext`r^3 - 3 $CellContext`r^4) 
               Cos[$CellContext`\[Theta]]^2 + $CellContext`a$1160^4 \
($CellContext`a$1160^2 $CellContext`M$1160 + 
                 2 $CellContext`M$1160^2 $CellContext`r - 
                 2 $CellContext`M$1160 $CellContext`r^2 + 3 $CellContext`r^3) 
                Cos[$CellContext`\[Theta]]^4 - $CellContext`a$1160^6 \
($CellContext`M$1160 - $CellContext`r) Cos[$CellContext`\[Theta]]^6 - 
               8 $CellContext`a$1160^2 $CellContext`M$1160^2 $CellContext`r^3 
               Sin[$CellContext`\[Theta]]^2 + 
               2 $CellContext`a$1160^4 $CellContext`M$1160^2 $CellContext`r 
                Sin[2 $CellContext`\[Theta]]^2) 
              Derivative[
               1][$CellContext`\[Phi]])))/(($CellContext`r^2 + \
$CellContext`a$1160^2 Cos[$CellContext`\[Theta]]^2) (
          2 $CellContext`a$1160^2 $CellContext`r^2 ($CellContext`a$1160^2 + 
            2 $CellContext`M$1160^2 - 
            2 $CellContext`M$1160 $CellContext`r + $CellContext`r^2) 
           Cos[$CellContext`\[Theta]]^2 + $CellContext`a$1160^4 \
($CellContext`a$1160^2 + $CellContext`r ((-2) $CellContext`M$1160 + \
$CellContext`r)) 
           Cos[$CellContext`\[Theta]]^4 + $CellContext`r^2 ($CellContext`r^3 \
((-2) $CellContext`M$1160 + $CellContext`r) + $CellContext`a$1160^2 (
              4 $CellContext`M$1160^2 + $CellContext`r^2) - 
            8 $CellContext`a$1160^2 $CellContext`M$1160^2 
            Cos[2 $CellContext`\[Theta]])))}, 
       Attributes[$CellContext`M$1160] = {Temporary}, 
       Attributes[$CellContext`a$1160] = {Temporary}, $CellContext`minkowski[]
         := Module[{$CellContext`g}, $CellContext`g = {{-1, 0, 0, 0}, {0, 1, 
           0, 0}, {0, 0, $CellContext`r^2, 0}, {
           0, 0, 0, $CellContext`r^2 
            Sin[$CellContext`\[Theta]]^2}}], $CellContext`findgeodesic[
         Pattern[$CellContext`g, 
          Blank[]]] := 
       Module[{$CellContext`metric = $CellContext`g, \
$CellContext`christoffel, $CellContext`geodesic, $CellContext`inversemetric}, \
$CellContext`inversemetric = 
          Inverse[$CellContext`metric]; $CellContext`christoffel = Simplify[
            
            Table[(1/2) 
             Sum[Part[$CellContext`inversemetric, $CellContext`i, \
$CellContext`s] (D[
                  Part[$CellContext`metric, $CellContext`s, $CellContext`j], 
                  Part[$CellContext`coords, $CellContext`k]] + D[
                  Part[$CellContext`metric, $CellContext`s, $CellContext`k], 
                  Part[$CellContext`coords, $CellContext`j]] - D[
                 Part[$CellContext`metric, $CellContext`j, $CellContext`k], 
                 Part[$CellContext`coords, $CellContext`s]]), {$CellContext`s,
                 1, $CellContext`n}], {$CellContext`i, 
              1, $CellContext`n}, {$CellContext`j, 
              1, $CellContext`n}, {$CellContext`k, 
              1, $CellContext`n}]]; $CellContext`geodesic = Simplify[
            
            Table[-Sum[
              Part[$CellContext`christoffel, $CellContext`i, $CellContext`j, \
$CellContext`k] Derivative[1][
                 Part[$CellContext`coords, $CellContext`j]] Derivative[1][
                 Part[$CellContext`coords, $CellContext`k]], {$CellContext`j, 
                1, $CellContext`n}, {$CellContext`k, 
                1, $CellContext`n}], {$CellContext`i, 
              1, $CellContext`n}]]], $CellContext`coords = {$CellContext`t, \
$CellContext`r, $CellContext`\[Theta], $CellContext`\[Phi]}, $CellContext`n = 
       4, $CellContext`trajectory[
         Pattern[$CellContext`inipos, 
          Blank[]], 
         Pattern[$CellContext`inivel, 
          Blank[]], 
         Pattern[$CellContext`udotu, 
          Blank[]], 
         Pattern[$CellContext`mass, 
          Blank[]], 
         Pattern[$CellContext`stepsi, 
          Blank[]], 
         Pattern[$CellContext`g, 
          Blank[]], 
         Pattern[$CellContext`geo, 
          Blank[]]] := 
       Module[{$CellContext`soln, $CellContext`xyzsoln, $CellContext`ics, \
$CellContext`ivs}, $CellContext`max\[Tau] = $CellContext`stepsi; \
$CellContext`\[Tau]Max = $CellContext`stepsi; $CellContext`ivs = \
$CellContext`inivel; $CellContext`M = $CellContext`mass; $CellContext`ics = \
$CellContext`inipos; $CellContext`uinvar = $CellContext`udotu; \
$CellContext`soln = $CellContext`computeSoln[$CellContext`max\[Tau], \
$CellContext`ivs, $CellContext`ics, $CellContext`g, $CellContext`geo]; \
$CellContext`soln = Flatten[$CellContext`soln]], $CellContext`computeSoln[
         Pattern[$CellContext`max\[Tau]i, 
          Blank[]], 
         Pattern[$CellContext`ivsi, 
          Blank[]], 
         Pattern[$CellContext`icsi, 
          Blank[]], 
         Pattern[$CellContext`metric, 
          Blank[]], 
         Pattern[$CellContext`geodesic, 
          Blank[]]] := 
       Module[{$CellContext`soln, $CellContext`ivs, $CellContext`ics, \
$CellContext`i, $CellContext`u0, $CellContext`tmp, $CellContext`u0solved, \
$CellContext`listeqns, $CellContext`deq}, $CellContext`ics = \
$CellContext`icsi; $CellContext`ivs = 
          Join[{$CellContext`u0}, $CellContext`ivsi]; $CellContext`tmp = \
$CellContext`metric; $CellContext`tmp = ReplaceAll[$CellContext`tmp, 
            Table[
            Part[$CellContext`coords, $CellContext`i] -> 
             Part[$CellContext`ics, $CellContext`i], {$CellContext`i, 
              0, $CellContext`n}]]; $CellContext`tmp = Dot[$CellContext`ivs, 
            Dot[$CellContext`tmp, $CellContext`ivs]]; $CellContext`u0solved = 
          Solve[$CellContext`tmp == $CellContext`uinvar, $CellContext`u0]; 
         Part[$CellContext`ivs, 1] = Last[
            
            ReplaceAll[$CellContext`u0, $CellContext`u0solved]]; \
$CellContext`listeqns = Flatten[
            Table[{Derivative[1][
                Part[$CellContext`coords, $CellContext`j]] -> Derivative[1][
                
                Part[$CellContext`coords, \
$CellContext`j]][$CellContext`\[Tau]], 
              Part[$CellContext`coords, $CellContext`j] -> 
              Part[$CellContext`coords, \
$CellContext`j][$CellContext`\[Tau]]}, {$CellContext`j, 
              1, $CellContext`n}]]; $CellContext`deq = Table[Derivative[2][
              Part[$CellContext`coords, $CellContext`i]][$CellContext`\[Tau]] == 
            ReplaceAll[
              
              Part[$CellContext`geodesic, $CellContext`i], \
$CellContext`listeqns], {$CellContext`i, 
             1, $CellContext`n}]; $CellContext`deq = Join[$CellContext`deq, 
            Table[Derivative[1][
               Part[$CellContext`coords, $CellContext`i]][0] == 
             Part[$CellContext`ivs, $CellContext`i], {$CellContext`i, 
              1, $CellContext`n}], 
            Table[
            Part[$CellContext`coords, $CellContext`i][0] == 
             Part[$CellContext`ics, $CellContext`i], {$CellContext`i, 
              1, $CellContext`n}]]; $CellContext`deq = 
          Flatten[{$CellContext`deq, 
             
             WhenEvent[$CellContext`r[$CellContext`\[Tau]] < 
              2 $CellContext`M + 
               0.1, $CellContext`\[Tau]Max = $CellContext`\[Tau]; 
              "StopIntegration"]}]; $CellContext`soln = 
          NDSolve[$CellContext`deq, $CellContext`coords, {$CellContext`\[Tau],
              0, $CellContext`max\[Tau]i}]], $CellContext`sphslnToCartsln[
         Pattern[$CellContext`soln, 
          Blank[]]] := 
       Block[{$CellContext`xs, $CellContext`ys, $CellContext`zs}, \
$CellContext`xs = ReplaceAll[$CellContext`r[$CellContext`\[Tau]] Sin[
              $CellContext`\[Theta][$CellContext`\[Tau]]] Cos[
              $CellContext`\[Phi][$CellContext`\[Tau]]], $CellContext`soln]; \
$CellContext`ys = ReplaceAll[$CellContext`r[$CellContext`\[Tau]] Sin[
              $CellContext`\[Theta][$CellContext`\[Tau]]] Sin[
              $CellContext`\[Phi][$CellContext`\[Tau]]], $CellContext`soln]; \
$CellContext`zs = ReplaceAll[$CellContext`r[$CellContext`\[Tau]] Cos[
              $CellContext`\[Theta][$CellContext`\[Tau]]], $CellContext`soln]; \
{$CellContext`xs, $CellContext`ys, $CellContext`zs}], $CellContext`animator[
         Pattern[$CellContext`soln, 
          Blank[]], 
         Pattern[$CellContext`cartsoln, 
          Blank[]], 
         Pattern[$CellContext`animdim, 
          Blank[]]] := 
       Module[{$CellContext`plotset, $CellContext`parameter, \
$CellContext`xyzsoln = $CellContext`cartsoln, $CellContext`row}, 
         If[$CellContext`uinvar == 0, $CellContext`parameter = 
           "\[Lambda] = ", $CellContext`parameter = "\[Tau] = "]; 
         If[$CellContext`animdim == "3D", $CellContext`plotset[
             Pattern[$CellContext`time, 
              Blank[]]] := {
             ParametricPlot3D[
              Evaluate[
               Flatten[{
                 Part[$CellContext`xyzsoln, 1], 
                 Part[$CellContext`xyzsoln, 2], 
                 Part[$CellContext`xyzsoln, 3]}]], {$CellContext`\[Tau], 
               0, $CellContext`time}, PerformanceGoal -> 
              "Quality"], $CellContext`starplot3d, 
             Graphics3D[{Red, 
               PointSize[Large], 
               Point[{
                 ReplaceAll[
                  
                  Part[$CellContext`xyzsoln, 
                   1], $CellContext`\[Tau] :> $CellContext`time], 
                 ReplaceAll[
                  
                  Part[$CellContext`xyzsoln, 
                   2], $CellContext`\[Tau] :> $CellContext`time], 
                 ReplaceAll[
                  
                  Part[$CellContext`xyzsoln, 
                   3], $CellContext`\[Tau] :> $CellContext`time]}]}]}, \
$CellContext`plotset[
             Pattern[$CellContext`time, 
              Blank[]]] := {$CellContext`starplot2d, 
             ParametricPlot[
              Evaluate[
               Flatten[{
                 Part[$CellContext`xyzsoln, 1], 
                 Part[$CellContext`xyzsoln, 2]}]], {$CellContext`\[Tau], 
               0, $CellContext`time}, PerformanceGoal -> "Quality"], 
             Graphics[{Red, 
               PointSize[Large], 
               Point[{
                 ReplaceAll[
                  
                  Part[$CellContext`xyzsoln, 
                   1], $CellContext`\[Tau] :> $CellContext`time], 
                 ReplaceAll[
                  
                  Part[$CellContext`xyzsoln, 
                   2], $CellContext`\[Tau] :> $CellContext`time]}]}]}]; \
$CellContext`row := $CellContext`parameter; Animate[
           Column[{
             TableForm[
              Join[{"Numerical values:", 
                Row[{$CellContext`row, $CellContext`time}]}, 
               $CellContext`coordlist[$CellContext`soln, $CellContext`time]]], 
             Show[
              $CellContext`plotset[$CellContext`time], Axes -> True, 
              PlotRange -> All, PerformanceGoal -> "Quality", 
              ImageSize -> {300, 300}]}], {{$CellContext`time, 
             0.1, $CellContext`row}, 0.1, $CellContext`\[Tau]Max}, 
           AnimationRate -> Automatic, AnimationRunning -> False, 
           AnimationRepetitions -> 1, DisplayAllSteps -> 
           True]], $CellContext`starplot3d = Graphics3D[
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