theta=Symbol('theta')
phi=Symbol('phi')
#general, spherically symmetric metric
gdd=Matrix((
(-B(r),0,0,0),
(0, A(r), 0, 0),
(0, 0, r**2, 0),
(0, 0, 0, r**2*sin(theta)**2)
))
g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Rie = Riemann(Gamma,X)
Ric=Ricci(Rie,X)
Rs =Rscalar(Ric)
print 'Initial metric:'
pprint(gdd)
Gamma.nonzero()
Ric.nonzero()
#Rie.nonzero()
Rs.printing()
print '-'*40
#Solving EFE for A and B
s = ( Ric.dd(1,1)/ A(r) ) + ( Ric.dd(0,0)/ B(r) )
pprint (s)
t = dsolve(s, A(r))
from ET import *
B = Function('B')
A = Function('A')
t = Symbol('t')
r = Symbol('r')
theta = Symbol('theta')
phi = Symbol('phi')
g = Metric((-B(r), 0, 0, 0), (0, A(r), 0, 0), (0, 0, r**2, 0),
(0, 0, 0, r**2 * sin(theta)**2))
x = (t, r, theta, phi)
C = Christoffel(g, x)
Rie = Riemann(C, x)
Ric = Ricci(Rie, x)
Rs = Rscalar(Ric)
G = ET(Ric, g, Rs)
print 'Initial metric:'
pprint(g.matrix())
#C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()
G.nonzero()
print 'Initial metric:'
pprint(gdd)
Gamma.nonzero()
Ric.nonzero()
import Ricci from sympy import * from sympy.abc import phi, theta coordinate = [theta, phi] g = Matrix([[1, 0], [0, sin(theta) * sin(theta)]]) S2 = Ricci.Ricci(coordinate, g) CF = S2.ChristoffelSymbol() print(CF)
