def from_metric(cls, metric):
"""
Get Schouten tensor calculated from a metric tensor
Parameters
----------
metric : ~einsteinpy.symbolic.metric.MetricTensor
Space-time Metric from which Christoffel Symbols are to be calculated
Raises
------
ValueError
Raised when the dimension of the tensor is less than 3
"""
if metric.dims >= 3:
t_ricci = RicciTensor.from_metric(metric)
r_scalar = RicciScalar.from_riccitensor(t_ricci,
parent_metric=None)
dims = metric.dims
t_schouten = (t_ricci.tensor() -
(r_scalar.expr * metric.lower_config().tensor() /
(2 * (dims - 1)))) / (dims - 2)
return cls(t_schouten,
metric.syms,
config="ll",
parent_metric=metric)
raise ValueError(
"Dimension of the space/space-time should be 3 or more")
def from_metric(cls, metric):
t_ricci = RicciTensor.from_metric(metric)
r_scalar = RicciScalar.from_riccitensor(t_ricci, t_ricci.parent_metric)
einstein_tensor = t_ricci.tensor() - (1 / 2) * metric.tensor() * r_scalar.expr
return cls(
einstein_tensor,
metric.syms,
config="ll",
parent_metric=t_ricci.parent_metric,
)