ChristoffelSymbols

Christoffel symbols of the first and second kind.

class gravica.christoffel.ChristoffelSymbols(metric)

Bases: object

Christoffel 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].