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Schwarzschild metric \( g = (1-\frac{r_\text{s}}{r})\,\mathrm dt\otimes\mathrm dt - \frac{1}{1-\frac{r_\text{s}}{r}}\,\mathrm dr\otimes \mathrm dr - r^2\,\mathrm d\theta\otimes \mathrm d\theta - r^2\sin^2\theta\,\mathrm d\phi\otimes \mathrm d\phi \).

Inverse Schwarzschild metric \( g = \frac{1}{1-\frac{r_\text{s}}{r}}\,\partial_t \otimes \partial_t - (1-\frac{r_\text{s}}{r})\,\partial_r \otimes \partial_r - \frac{1}{r^2}\,\partial_\theta \otimes \partial_\theta - \frac{1}{r^2\sin^2\theta}\,\partial_\phi \otimes \partial_\phi \).

Christoffel symbol of the Schwarzschild metric.

Ricci tensor of the Schwarzschild metric.

Einstein tensor of the Schwarzschild metric. The component functions evaluate to zero:

>>> let g = einstein 2
>>> g `evalSec` [1.1, 2.4, 1.7, 2.2]
ZeroTensor