## Abstract

We consider extremal black hole solutions to the vacuum Einstein equations in dimensions greater than five. We prove that the near-horizon geometry of any such black hole must possess an SO(2, 1) symmetry in a special case where one has an enhanced rotational symmetry group. We construct examples of vacuum near-horizon geometries using the extremal Myers-Perry black holes and boosted Myers-Perry strings. The latter lead to near-horizon geometries of black ring topology, which in odd spacetime dimensions have the correct number of rotational symmetries to describe an asymptotically flat black object. We argue that a subset of these correspond to the near-horizon limit of asymptotically flat extremal black rings. Using this identification we provide a conjecture for the exact "phase diagram" of extremal vacuum black rings with a connected horizon in odd spacetime dimensions greater than five.

Original language | English |
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Article number | 044042 |

Pages (from-to) | - |

Number of pages | 28 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 78 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2008 |

## Keywords

- Black holes
- EXTREMAL BLACK-HOLES
- SYMMETRY