In physics and astronomy, a Reissner-Nordström black hole, discovered by Gunnar Nordström and Hans Reissner, is a black hole that carries mass $M$, electric charge $Q$, and no angular momentum. 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:

$ds^2=-\backslash left(1-\backslash frac\{2M\}\{r\}+\backslash frac\{Q^2\}\{r^2\}\backslash right)dt^2\; +\; \backslash left(1-\backslash frac\{2M\}\{r\}+\backslash frac\{Q^2\}\{r^2\}\backslash right)^\{-1\}\; dr^2\; +r^2\; d\backslash Omega^2$

where we have used units with the speed of light and the gravitational constant equal to one ($c=G=1$) and where the angular part of the metric is

$d\backslash Omega^2\; =\; d\backslash theta^2\; +\backslash sin^2\backslash theta\backslash ,d\backslash phi^2$

The electromagnetic potential is

$A\; =\; \backslash left(\backslash frac\{Q\}\{r\},\; 0,\; 0,\; 0\backslash right)$.

While the charged black holes with (especially with $|Q|\; \backslash ll\; M$) are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon. As usual, the event horizons for the spacetime may be reliably located by analyzing the equation $g^\{00\}=0$. A brief look at this condition produces a quadratic in $r$ whose solutions show the event horizons to be located at

$r\_\backslash pm\; =\; M\; \backslash pm\; \backslash sqrt\{M^2-Q^2\}.$

These horizons become degenerate for $|Q|=M$ which is the case of an extremal black hole.

The black holes with $|Q|\; >\; M$ are believed not to exist in Nature because they would contain a naked singularity; their appearance would contradict Roger Penrose's cosmic censorship hypothesis which is generally believed to be true. Theories with supersymmetry usually guarantee that such "superextremal" black holes can't exist.

If magnetic monopoles are included into the theory, then a generalization to include magnetic charge $P$ is obtained by replacing $Q^2$ by $Q^2\; +\; P^2$ in the metric and including the term $P\; \backslash cos\; \backslash theta\; d\; \backslash phi$ in the electromagnetic potential.

External links

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• spacetime diagrams including Finkelstein diagram and Penrose diagram, by Andrew J. S. Hamilton

Exact solutions in general relativity | Black holes

Agujero negro de Reissner-Nordstrom