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Near horizon symmetries of extremal black holes

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Recently, an attractor mechanism for extremal, rotating black holes was demonstrated. The proof relied on the assumption that the near-horizon of an extermal black holes has an SO(2,1) isometry. After a basic review of near horizon geometries, I wlil prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as all known black holes in four and five dimensions. The result holds for a general two-derivative theory of gravity coupled to abelian gauge fields and neutral scalars, and remains stable to higher-derivative corrections. Finally I will demonstrate how one can use analytic continuation to relate SU(2)-invariant black hole solutions to SO(2,1)-symmetric near horizon geometries. The talk is based on work with J.Lucietti and H.S.Reall that appeared in arXiv:0705.4214

This talk is part of the DAMTP Friday GR Seminar series.

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