Yukterez

Schwarzschild black hole shadow, angular radius

May 25th, 2020
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  1. (* Angular radius of a Schwarzschild black hole shadow, schwarzschild.yukterez.net *)
  2.  
  3. r0=Infinity;
  4. rs=2; χ0=rs/r0; χ=rs/r; p=4/27;
  5.  
  6. α[n_]:=ArcCos[(χ^2 Sqrt[1-χ0] Sqrt[χ-χ0]+n Sqrt[p(χ^3-χ^2+p)])/(χ^3-χ0 χ^2+p)] 180/π;
  7. δ=If[D[α[-1],r]>0,Evaluate[α[+1]],Evaluate[α[-1]]];
  8.  
  9. Plot[δ, {r,0,10}, Frame->True,
  10. AspectRatio->1/3, ImageSize->500,
  11. GridLines->{{},{45}},
  12. PlotRange->{{0,10},{0,90}}]
  13.  
  14. N@Block[{r=10},δ]
  15. N@Block[{r=0.0000001},δ]
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