In[]:=
f[r_]:=1-
2M
r
+
2
Q
2
r
+
8
3
πP
2
r
​​mass=
3
2
Q
+3
2
r
+8Pπ
4
r
6r
/.rrh;​​T[r_]:=
-
2
Q
+
2
r
+8Pπ
4
r
4π
3
r
​​veff[r_]:=
f[r]
2
r
In[]:=
rp=r/.Last[NSolve[
∂
r
veff[r]0,r,Reals]]/.Mmass
Out[]=
0.25(3
2
Q
+3
2
rh
+8Pπ
4
rh
)
rh
+0.5
-8.
2
Q
+
0.25
2
(3
2
Q
+3
2
rh
+8Pπ
4
rh
)
2
rh
if
condition
In[]:=
rs=
rp
f[rp]
/.M0.9;​​Q=0.1;​​P=0.3315;​​min=FindMinimum[T[rh]/.{Q0.5,P0.1}&&0<rh<1,{rh,0.6}]​​max=FindMaximum[T[rh]/.{Q0.5,P0.1}&&0<rh<1,{rh,0.6}]​​rs/.rh->0.6​​rs/.rh->0.37​​T[0.37]​​T[0.6]
Out[]=
{0.444635,{rh0.369814}}
Out[]=
{0.526745,{rh0.6}}
Out[]=
0.599717
Out[]=
1.22686
Out[]=
0.444674
Out[]=
0.526745
In[]:=
plot=ParametricPlot[{rs*Cos[θ],rs*Sin[θ]},{rh,0.37,0.6},{θ,0,2*Pi},AxesFalse,ColorFunction->Function[{x,y,rh},ColorData["SunsetColors"][Rescale[T[rh],{T[0.37],T[0.6]}]]],PlotLegendsBarLegend[{"SunsetColors",{T[0.37],T[0.6]}},LegendLabel->Style[HoldForm[T],14]]]
Out[]=
T
In[]:=
{T[0.39],T[0.40],T[0.42],T[0.45],T[0.50],T[0.51],T[0.55],T[0.59]}
Out[]=
{0.4492,0.45171,0.457189,0.466456,0.484289,0.488165,0.504553,0.522172}
In[]:=
{rs/.rh->0.39,rs/.rh->0.4,rs/.rh->0.42,rs/.rh->0.45,rs/.rh->0.5,rs/.rh->0.51,rs/.rh->0.55,rs/.rh->0.59}
Out[]=
{0.902428,0.8298,0.742836,0.676199,0.627668,0.622295,0.608066,0.600862}