Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-09-16
Commun.Math.Phys.291:403-441,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30pp, Latex, no figures
Scientific paper
10.1007/s00220-009-0841-1
All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.
Hollands Stefan
Ishibashi Akihiro
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