Schwarzschild Spacetime.ipynb

Kernel: SageMath 8.2

%display latex

M = Manifold(4, 'M', latex_name=r'\mathcal{M}', structure='Lorentzian'); M

var('m', domain='real'); assume(m>0)

Sch.<t,r,th,ph> = M.chart(r't r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi'); Sch

g = M.metric()
g[0,0] = -(1 - 2*m/r)
g[1,1] = 1/(1 - 2*m/r)
g[2,2] = r^2
g[3,3] = (r*sin(th))^2
g.display()

nab = g.connection(); nab

nab(g) == 0

g.christoffel_symbols_display()