python_schw

from gravipy import *
#####################
# Coordinates (\chi is the four-vector of coordinates)
t, r, theta, phi, M = symbols('t, r, theta, phi, M') 
x = Coordinates('\chi', [t, r, theta, phi])
#####################
# Metric tensor
Metric = diag((1-2*M/r), -1/(1-2*M/r), -r**2, -r**2*sin(theta)**2)
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))
#####################