| Copyright | (c) 2019 Tobias Reinhart and Nils Alex |
|---|---|
| License | MIT |
| Maintainer | tobi.reinhart@fau.de, nils.alex@fau.de |
| Safe Haskell | None |
| Language | Haskell2010 |
Math.Tensor.Examples.Gravity.Schwarzschild
Description
This module provides the metric, inverse metric, Christoffel symbol, Ricci tensor and Einstein tensor for the Schwarzschild spacetime as an example for tensor sections and partial derivatives thereof.
Synopsis
- schwarzschild :: Floating a => a -> STTens 0 2 (CFun [a] a)
- schwarzschild' :: Floating a => a -> STTens 2 0 (CFun [a] a)
- christoffel :: forall a. Floating a => a -> STTens 1 2 (CFun [a] a)
- ricci :: forall a. Floating a => a -> STTens 0 2 (CFun [a] a)
- einstein :: forall a. Floating a => a -> STTens 0 2 (CFun [a] a)
Documentation
schwarzschild :: Floating a => a -> STTens 0 2 (CFun [a] a) Source #
Schwarzschild metric \( g = (1-\frac{r_\text{s}}{r})\,\mathrm dt\otimes\mathrm dt - \frac{1}{1-\frac{r_\text{s}}{r}}\,\mathrm dr\otimes \mathrm dr - r^2\,\mathrm d\theta\otimes \mathrm d\theta - r^2\sin^2\theta\,\mathrm d\phi\otimes \mathrm d\phi \).
schwarzschild' :: Floating a => a -> STTens 2 0 (CFun [a] a) Source #
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 :: forall a. Floating a => a -> STTens 1 2 (CFun [a] a) Source #
Christoffel symbol of the Schwarzschild metric.