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I am trying to find black hole shadow contour with respect to temperature. with metricf[r_] := -((2*M*r^2)/(g^3 + r^3)) + (8/3)*Pi*P*r^2 + 1. So here is my code,

f[r_] := 1 - (2*M*r^2)/(r^3 + g^3) + (8/3)*Pi*P*r^2; 
M = ((g^3 + r^3)*(8*Pi*P*r^2 + 3))/(6*r^2); 
T = (-(2*g^3) + 8*Pi*P*r^5 + r^3)/(4*Pi*r*(g^3 + r^3)); 
\[Xi] = ((3 + 8*Pi*r^2)^3*(g^3 + r^3)^3)/(216*r^6) + Sqrt[g^6 - 
(g^3*(3 + 8*Pi*r^2)^3*(g^3 + r^3)^3)/(108*r^6)] - g^3; 
rp = g^3/(2*r^2) + r/2 + (4/3)*(g^3 + r^3)*P*Pi + ((3 + 
8*Pi*r^2)^2*(g^3 + r^3)^2)/(36*r^4*\[Xi]^(1/3)) + \[Xi]^(1/3); 
rs = rp/Sqrt[f[rp]]; 
shadowcontour[met_, g_, p_, T1_, T2_] := Module[{T, r, \[Theta], 
shadowrad, photonrad, xi, rh}, 
rh = r /. Last[NSolve[T - (-2*g^3 + r^3 + 8*p*Pi*r^5)/(4*Pi*r*(g^3 + r^3)) == 0, r]]; 
xi = ((3 + 8*Pi*r^2)^3*(g^3 + r^3)^3)/(216*r^6) + Sqrt[g^6 - (g^3*(3 + 8*Pi*r^2)^3*(g^3 + r^3)^3)/(108*r^6)] - g^3; 
photonrad = g^3/(2*r^2) + r/2 + (4/3)*(g^3 + r^3)*p*Pi + ((3 + 8*Pi*r^2)^2*(g^3 + r^3)^2)/(36*r^4*xi^(1/3)) + xi^(1/3); 
shadowrad = photonrad/Sqrt[met[photonrad]] /. r -> rh; 
plot = Region[ParametricRegion[{shadowrad*Cos[\[Theta]], 
shadowrad*Sin[\[Theta]]}, {{\[Theta], 0, 2*Pi}, {T, T1, T2}}]]; 
plot]
shadowcontour[f, 0.3, 0.002418/0.09, 0, 0.21]

now perfomrfing shadowcontour[f, 0.3, 0.002418/0.09, 0, 0.21] gives no answer. Can anyone help me with it.

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  • $\begingroup$ You have 2 boxes with the code. If I copy and paste in my notebook, there are some undefined variables. Then I see that you have definition of f somewhere, and parameters g and P are defined yet in another place. I think you will get better answers if you prepare a single copy-paste-able code. $\endgroup$ Commented Apr 20, 2024 at 8:44
  • $\begingroup$ actually I am trying to recreate fig 5 in arxiv.org/pdf/2301.06120.pdf . They have used equation 16-21 and 24,25 to plot the figure with f(r0)=1 and the choice of P and g as mentioned. can you help me with it? $\endgroup$ Commented Apr 23, 2024 at 7:02
  • $\begingroup$ You should prepare a copy-paste-able code. Currently it consists of many pieces, extra work is needed to even start working on your problem. $\endgroup$ Commented Apr 23, 2024 at 8:23
  • $\begingroup$ Please look at This. There I have shared two of my notebook. community.wolfram.com/groups/-/m/t/3163006 $\endgroup$ Commented Apr 23, 2024 at 8:38
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    $\begingroup$ Kindly check the edited version. I have made the code in single box. Once again I apologize for rudeness and I will be careful from next time. Thank you. $\endgroup$ Commented Apr 24, 2024 at 7:01

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It is not the full answer, rather a suggestion how to organise the code. The problem with the existing code is in the mixing of notations. For instance, in the definition of f a parameter P is used, which is undefined. Later, a parameter p is used. In order to avoid this confusion, you have to explicitly specify all arguments. I recommend to define several functions:

 Clear[f,M,T,ξ,rp,rs]
f[r_,M_,g_,P_]:=1-(2*M[r,g,P]*r^2)/(r^3+g^3)+(8/3)*Pi*P*r^2;
M[r_,g_,P_]:=((g^3+r^3)*(8*Pi*P*r^2+3))/(6*r^2);
T[r_,g_,P_]:=(-(2*g^3)+8*Pi*P*r^5+r^3)/(4*Pi*r*(g^3+r^3));
ξ[r_,g_]:=((3+8*Pi*r^2)^3*(g^3+r^3)^3)/(216*r^6)+Sqrt[g^6-(g^3*(3+8*Pi*r^2)^3*(g^3+r^3)^3)/(108*r^6)]-g^3;
rp[r_,g_,P_]:=g^3/(2*r^2)+r/2+(4/3)*(g^3+r^3)*P*Pi+((3+8*Pi*r^2)^2*(g^3+r^3)^2)/(36*r^4*ξ^(1/3))+ξ^(1/3);
rs[r_,M_,g_,P_]:=rp[r,g,P]/Sqrt[f[rp[r,g,P],M,g,P]]
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