metric_field: Create a metric tensor field

In ricci: Ricci Calculus

Create a metric tensor field

Description

Metric tensors are an essential ingredient of (Pseudo-) Riemannian manifolds and define distance relations between points. They are used to define geometric tensors such as e.g. the Ricci curvature ricci(), and a metric connection, i.e. a covariant derivative. They are also essential for raising and lowering indices of tensor fields correctly when using non-flat coordinates.

Usage

metric_field(metric, metric_inv, coords)

Arguments

metric	A nxn matrix / array representing the covariant metric tensor components. The components are usually expressions as character strings formed from coordinates, since numeric values can only represent constant tensor fields.
metric_inv	A nxn matrix / array representing the contraviant metric tensor components, i.e. the inverse matrix of the covariant metric tensor component matrix.
coords	A character vector of n coordinate names that are used in the component expressions. This information is essential for forming symbolic derivatives.

Value

An object of class c("metric_field", "array") that represents the components of a metric tensor on a (Pseudo-) Riemannian manifold in a certain coordinate system specified by coords.

See Also

Wikipedia: Metric tensor

Other metric tensors: g_eucl_cart(), g_mink_cart(), g_sph(), g_ss()

ricci documentation built on Sept. 9, 2025, 5:56 p.m.