m = 1.;

rzero = 4.;

Kmax = (rzero^3/(2 m))^(1/2);

chizero = ArcSin[Sqrt[(2 m)/rzero]];

krokvp = 0.25;

rmax[r_Real, \[Tau]_Real, m_Real] := 
 FindRoot[\[Tau] == 
    Sqrt[rmax^3/(
      8 m)] (ArcCos[(2 r)/rmax - 1] + 
       Sqrt[1 - ((2 r)/ rmax - 1)^2]), {rmax, 
    If[r < 2 m, 3 m, r] }][[1, 2]]

\[Eta][r_Real, \[Tau]_Real, m_Real] := 
 ArcCos[(2 r)/rmax[r, \[Tau], m] - 1]

t[\[Eta]_Real, rmax_Real] := 
 2 m Log[Abs[((rmax/(2 m) - 1)^(1/2) + 
      Tan[\[Eta]/2])/((rmax/(2 m) - 1)^(1/2) - Tan[\[Eta]/2])]] + 
  2 m (rmax/(2 m) - 1)^(1/
   2) (\[Eta] + rmax/(4 m) (\[Eta] + Sin[\[Eta]]))

rStar[r_, M_] := r + 2 M Log[Abs[r/(2 M) - 1]]

\[Tau]povrch[r_Real] := 
 Kmax/2 ( ArcCos[r/Kmax*2/Sin[chizero] - 1] + 
    Sqrt[1 - (r/Kmax*2/Sin[chizero] - 1)^2])

\[Eta]in[\[Tau]_Real, am_Real] := 
 FindRoot[\[Tau] == am/2 (\[Eta] + Sin[\[Eta]]), {\[Eta], Pi/2} ][[1, 
   2]]

\[Chi]in[asin\[Chi]_Real, \[Tau]_Real, am_Real] := 
 ArcSin[(2 asin\[Chi])/(am (1 + Cos[\[Eta]in[\[Tau], am]]))]


ContourPlot[
 Evaluate@Table[
   rStar[r, m] - t[\[Eta][r, \[Tau], m], rmax[r, \[Tau], m]] == 
    rStar[parametr, m] - 
     t[\[Eta][parametr, \[Tau]povrch[parametr], m], 
      rmax[parametr, \[Tau]povrch[parametr], m]], {parametr, 0, 2 m, 
    krokvp}], {r, 0, 2 m }, {\[Tau], 0, 11}, ContourShading -> False, 
 ContourStyle -> {{Darker@Green, Opacity[0.4]}, {Darker@Green, 
    Opacity[0.4]}, {Darker@Green}}]
figVyletujiciVneA = %;

ContourPlot[
 Evaluate@Table[
   rStar[r, m] - t[\[Eta][r, \[Tau], m], rmax[r, \[Tau], m]] == 
    rStar[parametr, m] - 
     t[\[Eta][parametr, \[Tau]povrch[parametr], m], 
      rmax[parametr, \[Tau]povrch[parametr], m]], {parametr, 2 m, 
    rzero, krokvp}], {r, 2 m, 6 }, {\[Tau], 0, 11}, 
 ContourShading -> False, 
 ContourStyle -> {{Darker@Green}, {Darker@Green, 
    Opacity[0.4]}, {Darker@Green, Opacity[0.4]}}]
figVyletujiciVneB = %;


\[Epsilon] = +10^-10
KorekceNa2M = 
 SetPrecision[
  rStar[2 m + \[Epsilon], m] + 
   t[\[Eta][2 m + \[Epsilon], \[Tau]povrch[2 m + \[Epsilon]], m], 
    rmax[2 m + \[Epsilon], \[Tau]povrch[2 m + \[Epsilon]], m]], 7]

ContourPlot[
 Evaluate@Table[
   rStar[r, m] + t[\[Eta][r, \[Tau], m], rmax[r, \[Tau], m]] == 
    If[parametr == 2 m, KorekceNa2M, 
     rStar[parametr, m] + 
      t[\[Eta][parametr, \[Tau]povrch[parametr], m], 
       rmax[parametr, \[Tau]povrch[parametr], m]]], {parametr, 0, 
    rzero, krokvp}], {r, 0, 6 }, {\[Tau], 0, 11}, 
 ContourShading -> False, 
 ContourStyle -> {{Red, Opacity[0.4]}, {Red, Opacity[0.4]}, {Red}}]
figVletujiciVne = %;

ContourPlot[
 t[\[Eta][r, \[Tau], m], rmax[r, \[Tau], m]], {r, 0, 6 }, {\[Tau], 0, 
  11}, Contours -> Range[5, 22, 2.5], ContourShading -> False, 
 ContourStyle -> Blue, PlotPoints -> 50]
figSchwarzschildůvČasKonstantní = %;

ParametricPlot[{2, parametr}, {parametr, 0, 11}, 
 PlotStyle -> {Darker@Green, Thickness[0.007]}]
figHorizont = %;

RegionPlot[
 y <= Kmax/
   2 ( ArcCos[x/Kmax*2/Sin[chizero] - 1] + 
     Sqrt[1 - (x/Kmax*2/Sin[chizero] - 1)^2]), {x, 0, 6}, {y, 0, 11} ,
  PlotStyle -> LightGray, BoundaryStyle -> Black]
figKolabujiciPrach = %;

Ing[asin\[Chi]_Real, \[Tau]_Real, am_Real] := 
 Block[{w = {\[Chi]in[asin\[Chi], \[Tau], am] + \[Eta]in[\[Tau], 
       am]}}, If[\[Tau] < \[Tau]povrch[asin\[Chi]], w, Undefined]]

ContourPlot[
 Evaluate@Table[
   Ing[asin\[Chi], \[Tau], 
     Kmax] == \[Chi]in[parametr, \[Tau]povrch[parametr], Kmax] + 
     2 ArcCos[Sqrt[parametr/rzero]], {parametr, 0, rzero, 
    krokvp}], {asin\[Chi], 0, rzero }, {\[Tau], 0, 11}, 
 ContourShading -> False, 
 ContourStyle -> {{Red, Opacity[0.4]}, {Red, Opacity[0.4]}, {Red}}]
figVletujiciUvnitr = %;

Outg[asin\[Chi]_Real, \[Tau]_Real, am_Real] := 
 Block[{w = {\[Chi]in[asin\[Chi], \[Tau], am] - \[Eta]in[\[Tau], 
       am]}}, If[\[Tau] < \[Tau]povrch[asin\[Chi]], w, Undefined]]

ContourPlot[
 Evaluate@Table[
   Outg[asin\[Chi], \[Tau], 
     Kmax] == \[Chi]in[parametr, \[Tau]povrch[parametr], 
      Kmax] - \[Eta]in[\[Tau]povrch[parametr], Kmax], {parametr, 0, 
    rzero, krokvp}], {asin\[Chi], 0, rzero }, {\[Tau], 0, 11}, 
 ContourShading -> False, 
 ContourStyle -> {{Darker@Green, Opacity[0.4]}, {Darker@Green, 
    Opacity[0.4]}, {Darker@Green}}]
figVyletujiciUvnitr = %;


ParametricPlot[{parametr, 0}, {parametr, 0, rzero}, 
 PlotStyle -> Purple]
figPurpleLine = %;

ParametricPlot[{parametr, 0}, {parametr, rzero, 6}, 
 PlotStyle -> Orange]
figOrangeLine = %;

ParametricPlot[{0, parametr}, {parametr, 0, 11}, 
 PlotStyle -> {Black, Thickness[0.01]}]
TlustáČernáČára = %;

Show[ figVyletujiciVneA, figVyletujiciVneB, figVletujiciVne, \
figSchwarzschildůvČasKonstantní, figHorizont, figKolabujiciPrach, \
figVletujiciUvnitr, figVyletujiciUvnitr, figPurpleLine , \
figOrangeLine , TlustáČernáČára, ImageSize -> 500, 
 BaseStyle -> {FontFamily -> "Latin Modern Roman", FontSize -> 20}, 
 LabelStyle -> {GrayLevel[0]}, Frame -> {{True, True}, {True, True}}, 
 FrameLabel -> {{\[Tau]/M, None}, { OverTilde[\[Rho]]/M, None}}, 
 FrameTicks -> All, RotateLabel -> False, 
 PlotRange -> {{0, 6}, {0, 11}}]