New Restrictions on the Topology of Extreme Black Holes

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.

11 pages; minor improvements

References in corpus (11)

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Cited by in corpus (7)

• Isotropic quasi-Einstein manifolds
• Electrovacuum spacetime near an extreme horizon
• A Bakry-Émery Almost Splitting Result With Applications to the Topology of Black Holes
• On the nonexistence of extreme anti-de Sitter black rings
• Black Lenses in Kaluza-Klein Matter
• Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary
• On Nilpotent and Solvable Quasi-Einstein Manifolds