g_ss: Schwarzschild metric tensor

In ricci: Ricci Calculus

Schwarzschild metric tensor

Description

Provides the metric tensor of the Einstein equation's Schwarzschild solution in Schwarzschild coordinates where the Schwarzschild radius r_s is set to 1.

ds^2 = - \left(1-\frac{r_s}{r}\right) dt^2 + \left(1-\frac{r_s}{r}\right)^{-1} dr^r + r^2 d\Omega^2

Usage

g_ss(n, coords = c("t", "r", paste0("ph", 1:(n - 2))))

Arguments

n	The dimension of the metric tensor.
coords	A character vector of coordinate names. The length needs to match the tensor dimensions.

Details

Note that Schwarzschild coordinates become singular at the Schwarzschild radius (event horizon) r=r_s=1 and at r=0.

Value

The covariant metric tensor as array imputed with coordinate names.

See Also

Wikipedia: Schwarzschild metric

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

Examples

g_ss(4)
g_ss(4) %_% .(+i, +j)

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