RiemannTensor¶
Riemann curvature tensor.
- class gravica.riemann.RiemannTensor(christoffel)¶
Bases:
objectRiemann curvature tensor \(R^a_{\ bcd}\).
\[R^a_{\ bcd} = \partial_c\,\Gamma^a_{\ db} - \partial_d\,\Gamma^a_{\ cb} + \Gamma^a_{\ ce}\,\Gamma^e_{\ db} - \Gamma^a_{\ de}\,\Gamma^e_{\ cb}\]- classmethod from_metric(metric)¶
Build from a
MetricTensor.- Return type:
- property components: list[list[list[list[Expression]]]]¶
\(R^a_{\ bcd}\) indexed as
[a][b][c][d].
- fully_contravariant(a, b, c, d)¶
\(R^{abcd} = g^{ae}\,g^{bf}\,g^{cg}\,g^{dh}\,R_{efgh}\).
- Return type:
Expression
- fully_covariant(a, b, c, d)¶
\(R_{abcd} = g_{ae}\,R^e_{\ bcd}\).
- Return type:
Expression