Extreme 5-dimensional black holes with SU(2)-symmetric horizons

TL;DR

This paper proves that the near horizon geometry of certain 5-dimensional extreme vacuum black holes with SU(2) symmetry is necessarily that of a Berger sphere, regardless of the cosmological constant.

Contribution

It establishes a classification result for the near horizon geometries of 5D extreme black holes with SU(2) symmetry, showing they must be Berger spheres.

Findings

Near horizon geometry is a Berger sphere.

Applicable to black holes with or without cosmological constant.

Provides a geometric classification of these black holes.

Abstract

We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit $\SU(2)$ symmetry must be that of a Berger sphere.