MadSci Network: Physics

Re: What are the properties of a Kerr-Newman black hole

Date: Fri Jan 19 13:01:50 2007
Posted By: Michael Wohlgenannt, PostDoc
Area of science: Physics
ID: 1164034451.Ph

Dear N.N.,

all known stationary black hole solutions to the Einstein-Maxwell equations are special cases of the Kerr-Newman solution. It is described by only three parameters (cosmic censorship): the mass M, its charge Q and the quotient of angular momentum and mass, a = J/M. The singularity has the form of a ring, as in the case of the Kerr-solution (Q=0). This ring lies within the black hole. If the mass satisfies the inequality

M^2 => Q^2 + a^2

the solution will have two horizons with radii

M + ( M^2 - a^2 - Q^2 )^(1/2) and
M - ( M^2 - a^2 - Q^2 )^(1/2).

Otherwise the singularity is "naked", i.e., not hidden from the outside by a horizon. There is also an ergosphere: it is situated in between the outer horizon and the "static limit", an ellipsoid defined by its distance from the center

r = M + ( M^2 - Q^2 - a^2 cos^2 (s) )^(1/2),

where s is the azimuthal angle. So the global structure is the same as in the case of a Kerr black hole.

For detailed information on Kerr-Newman black holes see for example the following books:

Gravitation by Misner, Thorne and Wheeler

General Relativity by R. Wald

inside a black hole.

I hope this helps,

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