
A charged, non-rotating black hole solution to the Einstein-Maxwell equations.The Reissner–Nordström black hole is a solution to Einstein's equations that describes a non-rotating, electrically charged black hole. Unlike the simpler Schwarzschild black hole, which is characterized only by mass, this solution includes an electric charge, making it a more complete theoretical object. It is a static, spherically symmetric solution to the Einstein–Maxwell equations, meaning it accounts for both gravity and electromagnetism.
The solution was independently discovered by Hans Reissner (1916) and Gunnar Nordström (1918), shortly after Schwarzschild's solution. It was one of the first exact solutions to Einstein's field equations beyond the vacuum case.
The solution arises from combining general relativity with Maxwell's equations of electromagnetism. The charge creates an electric field that contributes to the stress-energy tensor, which in turn curves spacetime. This results in a geometry with two horizons (inner and outer) for a charge less than the mass, unlike the single horizon of a Schwarzschild black hole. The outer horizon is the event horizon, while the inner horizon is a Cauchy horizon, where causality may break down.
While real astrophysical black holes are expected to be nearly neutral, the Reissner–Nordström solution is used as a theoretical laboratory for studying quantum gravity, black hole thermodynamics, and the information paradox.
For a charge greater than the mass (in geometric units), the Reissner–Nordström solution has no event horizon, leaving a naked singularity — a possibility that the cosmic censorship conjecture forbids.









