Contents Online

# Advances in Theoretical and Mathematical Physics

## Volume 23 (2019)

### Number 7

### Electrovacuum spacetime near an extreme horizon

Pages: 1903 – 1950

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n7.a5

#### Authors

#### 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 $\operatorname{AdS}_2 \times S^2$ 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‑$\operatorname{AdS}$ horizon. Finally, we completely classify transverse deformations of extreme horizons in three-dimensional Einstein–Maxwell theory with a negative cosmological constant.

Published 15 May 2020