reissner-nordstrm black hole

In physics and astronomy, a Reissner-Nordstrm black hole is a black hole that carries electric charge

Q

, no angular momentum, and mass

M

. 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-Nordstrm metric that generalizes the Schwarzschild metric of an electrically neutral black hole:

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

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\Omega^2 \equiv d\theta^2 +\sin^2 \theta\cdot d\phi^2

While the charged black holes with

Q < M

(especially with

Q << M

) are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon. These horizons merge 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.

External links

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

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