New Restrictions on the Topology of Extreme Black Holes

TL;DR

This paper establishes new topological restrictions on the horizon cross-sections of extreme stationary vacuum black holes across arbitrary dimensions, using geometric and topological methods without symmetry assumptions.

Contribution

It introduces bounds on Betti numbers and fundamental group structures for black hole horizons via novel geometric correspondences and splitting theorems, extending previous results.

Findings

Bounds on the first Betti number of horizon cross-sections

Restrictions on the fundamental group of black hole horizons

Refined classifications of possible horizon topologies

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.