Schwarzschild metric

The Schwarzschild metric was calculated by Karl Schwarzschild^[1] as a solution to Einstein's field equations in 1916. Also known as Schwarzschild solution, it is an equation from general relativity in the field of astrophysics. A metric refers to an equation which describes spacetime; in particular, a Schwarzschild metric describes the gravitational field around a Schwarzschild black hole - a non-rotating, spherical black hole with no magnetic field, and where the cosmological constant is zero.

It is essentially an equation that describes how a particle moves through the space near a black hole.

${\displaystyle (ds)^{2}=-c^{2}(1-{\frac {2GM}{rc^{2}}})(dt)^{2}+{\frac {1}{(1-{\frac {2GM}{rc^{2}}})}}(dr)^{2}+r^{2}(d\theta )^{2}+r^{2}\sin ^{2}(\theta )(d\phi )^{2}}$

1. ↑ Schwarzschild, K. (1999). "On the gravitational field of a sphere of incompressible fluid according to Einstein's theory". arXiv:physics/9912033.