Electrovacuum spacetime near an extreme horizon

TL;DR

This paper classifies all infinitesimal axisymmetric transverse deformations of extreme horizons in Einstein-Maxwell theory, revealing families of solutions including known black hole configurations and their generalizations, with implications for horizon stability and uniqueness.

Contribution

It provides a comprehensive classification of axisymmetric transverse deformations of extreme horizons in Einstein-Maxwell theory, including new families of solutions and uniqueness results.

Findings

Identified a two-parameter family of static deformations of AdS2 x S2 horizons.

Found a three-parameter family of deformations of extreme Kerr-Newman horizons.

Proved uniqueness of axisymmetric deformations for Kerr-AdS horizons.

Abstract

We determine all infinitesimal transverse deformations of extreme horizons in Einstein-Maxwell theory that preserve axisymmetry. In particular, we show that the general static transverse deformation of the AdS(2) X S(2) near-horizon geometry is a two-parameter family, which contains the known extreme charged, accelerating, static black hole solution held in equilibrium by an external electric or magnetic field (Ernst solution) and a special case of the extreme Kerr-Newman-Melvin solution. More generally, we find a three-parameter family of deformations of the extreme Kerr-Newman horizon, which contains the extreme Kerr-Newman-Melvin solution and a rotating generalisation of the Ernst solution. We also consider vacuum gravity with a cosmological constant and prove uniqueness of axisymmetric transverse deformations of the extreme Kerr-AdS horizon. Finally, we completely classify transverse deformations of extreme horizons in three-dimensional Einstein-Maxwell theory with a negative cosmological constant.