opensourceGR/python_kerr at master · tbirkandan/opensourceGR · GitHub

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from gravipy import *
#####################
# Coordinates (\chi is the four-vector of coordinates)
t, r, theta, phi, M, a, rhosq, Delta = symbols('t, r, theta, phi, M, a, rhosq, Delta')
x = Coordinates('\chi', [t, r, theta, phi])
#####################
# Metric tensor
rhosq = r**2+(a**2)*cos(theta)**2
Delta = r**2-2*M*r+a**2
Metric = Matrix([[(1-(2*M*r)/rhosq),0,0,(2*a*M*r*sin(theta)**2)/rhosq],[0,-rhosq/Delta,0,0],[0,0,-rhosq,0],[(2*a*M*r*sin(theta)**2)/rhosq,0,0,-(sin(theta)**2)*((r**2+a**2)+(2*(a**2)*M*r*sin(theta)**2)/rhosq)]])
g = MetricTensor('g', x, Metric)
#####################
# Christoffel symbols
Ga = Christoffel('Ga', g)
# Display all components
print(Ga(All, All, All))
# Display a single component
print(Ga(1,2,1))
#####################
# Ricci tensor
Ri = Ricci('Ri', g)
# Display all components
print(Ri(All, All))
# Display a single component
print(Ri(1, 2))
#####################
# Einstein tensor
G = Einstein('G', Ri)
# Display all components
print(G(All, All))
# Display a single component
print(G(3, 3))
#####################