New restrictions on the topology of extreme black holes

Marcus Khuri; Eric Woolgar; William Wylie

doi:10.1007/s11005-018-1121-9

New restrictions on the topology of extreme black holes

Marcus Khuri, Eric Woolgar, William Wylie

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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)
Pages (from-to)	661-673
Number of pages	13
Journal	Letters in Mathematical Physics
Volume	109
Issue number	3
DOIs	https://doi.org/10.1007/s11005-018-1121-9
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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10.1007/s11005-018-1121-9

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AU - Woolgar, Eric

AU - Wylie, William

PY - 2019/3/4

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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 - Splitting theorem

KW - m-Quasi-Einstein metric

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JF - Letters in Mathematical Physics

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New restrictions on the topology of extreme black holes

Abstract

Keywords

ASJC Scopus subject areas

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