科研之友
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摘要
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) x T (D-4), or S (3) x 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 a parts per thousand yen 6 seem to arise as the near-horizon limits of known black hole solutions.
- 出版日期2010-5
