On the 'Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

Hollands, Stefan and Ishibashi, Akihiro 2009. On the 'Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions. Communications in Mathematical Physics 291 (2) , pp. 443-471. 10.1007/s00220-009-0841-1

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Abstract

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 [24] 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Publisher:	Springer Verlag
ISSN:	0010-3616
Last Modified:	04 Feb 2018 01:24
URI:	https://orca.cardiff.ac.uk/id/eprint/13176

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