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In physics and astronomy, a Reissner-Nordstrøm black hole is a black hole that carries electric charge <math>Q<math>, no angular momentum, and mass <math>M<math>. 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-Nordstrøm metric that generalizes the Schwarzschild metric of an electrically neutral black hole:
- <math>ds^2=-\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)^{-1} dr^2 +r^2 d\Omega^2 <math>
where we have used units with the speed of light and the gravitational constant equal to one (<math>c=G=1<math>) and where the angular part of the metric is
- <math>d\Omega^2 \equiv d\theta^2 +\sin^2 \theta\cdot d\phi^2<math>
The electromagnetic potential is
- <math>A = -\frac{Q}{r}dt<math>.
While the charged black holes with <math>|Q| < M<math> (especially with <math>|Q| << M<math>) are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon. The horizons are located at <math>r = r_\pm := M \pm \sqrt{M^2-Q^2}<math>. These horizons merge for <math>|Q|=M<math> which is the case of an extremal black hole.
The black holes with <math>|Q| > M<math> 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.
External links
- spacetime diagrams (http://casa.colorado.edu/~ajsh/rn.html) including Finkelstein diagram and Penrose diagram, by Andrew J. S. Hamilton