All vacuum near horizon geometries in D-dimensions with (D - 3) commuting rotational symmetries

Hollands, Stefan and Ishibashi, Akihiro 2010. All vacuum near horizon geometries in D-dimensions with (D - 3) commuting rotational symmetries. Annales Henri Poincare 10 (8) , pp. 1537-1557. 10.1007/s00023-010-0022-y

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Abstract

We explicitly construct all stationary, non-static, extremal near horizon geometries in D dimensions that satisfy the vacuum Einstein equations, and that have D−3 commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in D = 4,5. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology S 2 × T D-4, or S 3 × T D-5, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as (D − 2)(D − 3)/2 continuous parameters. Not all of our metrics in D ≥ 6 seem to arise as the near-horizon limits of known black hole solutions.

Item Type:	Article
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	1424-0637
Last Modified:	04 Feb 2018 01:38
URI:	https://orca.cardiff.ac.uk/id/eprint/13879

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