ChristoffelSymbols¶
Christoffel symbols of the first and second kind.
- class gravica.christoffel.ChristoffelSymbols(metric)¶
Bases:
objectChristoffel symbols computed from a metric tensor.
\[\Gamma_{abc} = \tfrac{1}{2}(\partial_b\, g_{ac} + \partial_c\, g_{ab} - \partial_a\, g_{bc}) \quad\text{(first kind)}\]\[\Gamma^a_{\ bc} = g^{ad}\,\Gamma_{dbc} \quad\text{(second kind)}\]- property first_kind: list[list[list[Expression]]]¶
\(\Gamma_{abc}\) indexed as
[a][b][c].
- property second_kind: list[list[list[Expression]]]¶
\(\Gamma^a_{\ bc}\) indexed as
[a][b][c].