MathLiveSchwarzschild metric
This is the line element of the spacetime outside a spherically symmetric, non-rotating, uncharged mass, as a solution of Einstein's field equations with zero cosmological constant. It is used to describe the gravitational field around stars and black holes and to compute effects such as gravitational time dilation.
\mathrm{d}s^2=-\left(1-\frac{r_{\mathrm{S}}}{r}\right)c^2\,\mathrm{d}t^2+\left(1-\frac{r_{\mathrm{S}}}{r}\right)^{-1}\mathrm{d}r^2+r^2\,\mathrm{d}\Omega^2What the symbols mean
| spacetime interval (line element) along a path (\mathrm{m}); for timelike paths it equals c times proper time | |
| speed of light in vacuum (\mathrm{m/s}) | |
| Schwarzschild radius, \frac{2GM}{c^2} (\mathrm{m}) | |
| radial coordinate (\mathrm{m}) | |
| coordinate time (\mathrm{s}) | |
| line element on the unit two-sphere, \mathrm{d}\theta^2+\sin^2\theta\,\mathrm{d}\phi^2 |
About this formula
- FieldPhysics
- TopicGeneral relativity
- LevelAdvanced
- Also calledSchwarzschild solution, Schwarzschild line element, Schwarzschild spacetime, spherically symmetric vacuum solution, Schwarzschild black hole metric
- SourceWikidata Q742969
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