MetricTensor

Metric tensor and symbolic matrix utilities for GR.

gravica.metric.symbolic_det(matrix)

Compute the determinant of a symbolic square matrix via Laplace expansion.

Return type:

Expression

gravica.metric.symbolic_inverse(matrix)

Compute the inverse of a symbolic square matrix using cofactors.

Return type:

list[list[Expression]]

class gravica.metric.MetricTensor(components, coords)

Bases: object

A metric tensor \(g_{ab}\) for a given coordinate system.

Parameters:

• components (list[list[Expression]]) – NxN symmetric matrix of Expression entries.

• coords (tuple[Expression, ...]) – Coordinate symbols, e.g. (t, r, theta, phi).

property inverse: list[list[Expression]]

Compute \(g^{ab}\) (cached).

inv(a, b)

\(g^{ab}\).

Return type:

Expression

property det: Expression

\(\det(g_{ab})\) (cached).

is_diagonal()

Return type:

bool