### Abstract

We provide bounds on the first Betti number and structure results for the fundamental group of horizon cross sections for extreme stationary vacuum black holes in arbitrary dimension, without additional symmetry hypotheses. This is achieved by exploiting a correspondence between the associated near-horizon geometries and the mathematical notion of m-quasi-Einstein metrics, in addition to generalizations of the classical splitting theorem from Riemannian geometry. Consequences are analyzed and refined classifications are given for the possible topologies of these black holes.

Original language | English (US) |
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Pages (from-to) | 661-673 |

Number of pages | 13 |

Journal | Letters in Mathematical Physics |

Volume | 109 |

Issue number | 3 |

DOIs | |

State | Published - Mar 4 2019 |

### Keywords

- Black holes
- Horizon topology
- Splitting theorem
- m-Quasi-Einstein metric

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Khuri, M., Woolgar, E., & Wylie, W. (2019). New restrictions on the topology of extreme black holes.

*Letters in Mathematical Physics*,*109*(3), 661-673. https://doi.org/10.1007/s11005-018-1121-9