Reissner–Nordström metric

The Reissner - Nordström metric (after Hans Reissner and Gunnar Nordström ) describes electrically charged, non- rotating black holes. Mathematically speaking, it is an exact solution of the Einstein equations, which is uniquely determined by the following properties:

• Asymptotically flat
• Static
• Spherically - symmetric

Line element

The line element of the Reissner - Nordström metric has the form:

Wherein the ground and the electric charge ( in CGS units ) are of the object. In the so-called natural units is set so that the metric in the form of

Can be written ( as also in the following section). For simplicity, an electric point charge is assumed at the origin. Magnetic fields and circulating currents are neglected. The electromagnetic four-potential is thus a Coulomb potential:

Horizons and singularities

As with the Schwarzschild metric of the event horizon is that of the radius, where the metric is singular. This means

Due to the quadratic dependence on the radius r, however, there are two solutions of this equation. Therefore, there is an event horizon, and an additional case with Cauchy horizon lying further inside.

For the case

If the root is imaginary, so there is no horizon. One speaks in this case of a naked singularity, which in today's opinion, however, can not exist ( "Cosmic Censorship " hypothesis). Modern supersymmetric theories prohibit generally.

For the Reissner - Nordström metric turns into the Schwarzschild metric. Your singularities come in at and.

In astrophysics electrically charged black holes play (including the Kerr-Newman metric ) a subordinate role, because it is believed that each charge of the hole is quickly neutralized by electrical currents, namely the Akkretionsflüsse.

Swell

• Andreas Müller - Encyclopedia of Astrophysics - Reissner - Nordstrøm solution