In[]:=
γ=2;​​Κ=200;​​α=200;​​k=8π;​​EoS=P[r]-Κ*ρ[r]^γ==0;​​(*InvEos=ρ[r_]=(P[r]/Κ)^(1/γ);*)​​eq1=ϕ[r]-(2α*R[r]+1)==0​​eq2=-λ'[r]+(1/(2rϕ[r]+ϕ'[r]r^2))*((1-2M[r]/r)^(-1)*(k*(P[r]/Κ)^(1/γ)r^2-1/8α*(ϕ[r]-1)^2*r^2-ϕ[r])+ϕ[r]+2r*ϕ'[r](rν'[r]+1)+ϕ''[r]r^2)==0//Simplify​​eq3:=ν'[r]=(1/(2rϕ[r]+ϕ'[r]r^2))*((1-2M[r]/r)^(-1)*(k*P[r]*r^2+1/8α*(ϕ[r]-1)^2*r^2+ϕ[r])-ϕ[r]-2r*ϕ'[r]+2λ'[r]*ϕ'[r])//Simplify​​
Out[]=
-400R[r]+2αR[r]0
Out[]=
True
In[]:=
eq4=P'[r]==-(P[r]+(P[r]/Κ)^(1/γ))*ν'[r]
Out[]=
400ρ[r]
′
ρ
[r]-200
2
ρ[r]
-
2
ρ[r]
-1-2αR[r]+
r+2rαR[r]+100
3
r
2
αR[r]
+1600π
3
r
2
ρ[r]
r-2M[r]
-4r
′
αR
[r]+2
′
αR
[r]1+2αR[r]-
r+2rαR[r]+100
3
r
2
αR[r]
-8π
3
r
2
ρ[r]
r-2M[r]
+4r(1+
′
rν
[r])
′
αR
[r]+2
2
r
′′
αR
[r](rϕ[r]+
2
r
′
αR
[r])(2(rϕ[r]+
2
r
′
αR
[r]))
In[]:=
Model[p0_]:=NDSolve[{eq1,eq2,eq3,ϕ'[0]=1,λ[0]==0,ν[0]==0},{ϕ,λ,ν},{r,0.5,20}]
In[]:=
Model[0.02]
Set
:Tag Function in (2
′
αR
[#1]&)[0] is Protected.
NDSolve
:Equation or list of equations expected instead of True in the first argument -400R[r]+2αR[r]0,True,
-1-2αR[r]+
1
r11
-4r
′
αR
[r]+
2
′
αR
[r]1+4+2
2
r
′′
αR
[r]
rϕ[r]+Power[2]
(1)
1
[1]
2rϕ[r]+
2
r
′
αR
[r]
,1,λ[0]0,ν[0]0.
Out[]=
NDSolve-400R[r]+2αR[r]0,True,-1-2αR[r]+
r+2rαR[r]+100
3
r
2
αR[r]
+1600π
3
r
2
ρ[r]
r-2M[r]
-4r
′
αR
[r]+2
′
αR
[r]1+2αR[r]-
r+2rαR[r]+100
3
r
2
αR[r]
-8π
3
r
2
ρ[r]
r-2M[r]
+4r(1+
′
rν
[r])
′
αR
[r]+2
2
r
′′
αR
[r](rϕ[r]+
2
r
′
αR
[r])(2(rϕ[r]+
2
r
′
αR
[r])),1,λ[0]0,ν[0]0,{ϕ,λ,ν},{r,0.5,20}