Uniqueness of extreme horizons in Einstein-Yang-Mills theory

TL;DR

This paper proves that stationary extreme black holes in Einstein-Yang-Mills theory with a negative cosmological constant have near-horizon geometries uniquely matching the abelian embedded extreme Kerr-Newman black hole, with static cases forming a simple product space.

Contribution

It establishes the uniqueness of near-horizon geometries for extreme black holes in Einstein-Yang-Mills theory, extending known results to include negative cosmological constants.

Findings

Axisymmetric extreme black holes have AdS(2) symmetry in their near-horizon region.

Near-horizon geometry of static black holes is a direct product of AdS(2) and a constant curvature space.

The near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman black hole.

Abstract

We consider stationary extreme black hole solutions to the Einstein-Yang-Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS(2) symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We also show that the near-horizon geometry of any static black hole is a direct product of AdS(2) and a constant curvature space.