### 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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Journal | Letters in Mathematical Physics |

DOIs | |

State | Accepted/In press - Jan 1 2018 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*. https://doi.org/10.1007/s11005-018-1121-9

**New restrictions on the topology of extreme black holes.** / Khuri, Marcus; Woolgar, Eric; Wylie, William.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - New restrictions on the topology of extreme black holes

AU - Khuri, Marcus

AU - Woolgar, Eric

AU - Wylie, William

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Black holes

KW - Horizon topology

KW - m-Quasi-Einstein metric

KW - Splitting theorem

UR - http://www.scopus.com/inward/record.url?scp=85050772409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050772409&partnerID=8YFLogxK

U2 - 10.1007/s11005-018-1121-9

DO - 10.1007/s11005-018-1121-9

M3 - Article

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -