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.
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()