General Relativity/Reissner-Nordström black hole

<General Relativity

Reissner-Nordström black hole is a black hole that carries electric charge , no angular momentum, and mass . General properties of such a black hole are described in the article charged black hole.

It is described by the electric field of a point-like charged particle, and especially by the Reissner-Nordström metric that generalizes the Schwarzschild metric of an electrically neutral black hole:

where we have used units with the speed of light and the gravitational constant equal to one () and where the angular part of the metric is

The electromagnetic potential is


While the charged black holes with (especially with ) are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon. The horizons are located at . These horizons merge for which is the case of an extremal black hole.