Source code for einsteinpy.symbolic.predefined.godel
from sympy import Rational, diag, exp, sqrt, symbols
from einsteinpy.symbolic.metric import MetricTensor
[docs]
def Godel():
"""
Godel metric
Rev. Mod. Phys., v21, p447, (1949)
Stephani (10.25) 122
"""
coords = symbols("t x y z")
om = symbols("omega")
t, x, y, z = coords
# define the metric
metric = diag(-1, 1, -Rational(1, 2) * exp(2 * sqrt(2) * om * x), 1)
metric[0, 2] = metric[2, 0] = -exp(sqrt(2) * om * x)
metric = metric.tolist()
return MetricTensor(metric, coords, "ll", name="GodelMetric")