Here is my script:
print("Initialization of manifold, chart, and metric. Definitions of
constants.")
M=Manifold(4,'M',structure='Lorentzian')
X.<t,r,th,ph> = M.chart(r"t r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi")
(m,L,A,alpha,beta,r,th)=var('m,L,A,alpha,beta,r,th')
def G(r):
return 1-alpha*(1-exp(-beta*m/(alpha*r^3)))
g=M.metric()
g[0,0]=-(1-2*m*r^4/(r^3+2*m*L^2)/(r^2+A^2*cos(th)^2))*G(r)
g[0,3]=-2*A*m*r^4/(r^3+2*m*L^2)*sin(th)^2/(r^2+A^2*cos(th)^2)*G(r)
g[3,0]=g[0,3]
g[1,1]=(r^2+A^2*cos(th)^2)/(r^2-2*m*r^4/(r^3+2*m*L^2)+A^2)
g[2,2]=r^2+A^2*cos(th)^2
g[3,3]=sin(th)^2*(r^2+A^2+2*A^2*m*r^4*sin(th)^2/(r^3+2*m*L^2)/(r^2+A^2*cos(th)^2))*G(r)
print('Calculating Riemann tensor')
R=g.riemann()
print('Calculating Kretschmann scalar')
dR=R.down(g)
uR=R.up(g)
kr=uR['^{abcd}']*dR['_{abcd}']
print('Plot Kretschmann scalar')
maxima.plot3d(kr.expr().subs(m=10,L=1,A=6,alpha=2,beta=4),[r,0,3],[th,0,3.14]);
print("Limit at the origin of the Kretschmann scalar from theta=0")
print(limit(limit(kr.expr().subs(m=10,L=1,A=6,alpha=2,beta=4),th=0),r=0))
print("Limit at the origin of the Kretschmann scalar from theta=pi")
print(limit(limit(kr.expr().subs(m=10,L=1,A=6,alpha=2,beta=4),th=pi),r=0))
Il giorno venerdì 20 dicembre 2019 11:11:46 UTC+1, Jori Mäntysalo (TAU) ha
scritto:
>
> On Thu, 19 Dec 2019, Mattia Villani wrote:
>
> > Condition of type: STORAGE-EXHAUSTED
>
> > Changing the program problably is not the solution, since I am
> calculating
> > the Kretschmann scalar of a metric, which is the square of the curvature
>
> What function are you using? For example SageMath contains Maxima and one
> can increase it's stack size by
>
> maxima._eval_line(":lisp (ext:set-limit 'ext:heap-size 1000000)",
> wait_for_prompt=False)
>
> but propably you use some other part of Sage.
>
> --
> Jori Mäntysalo
>
> Tampereen yliopisto - Ihminen ratkaisee
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