Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 7

Electrovacuum spacetime near an extreme horizon

Pages: 1903 – 1950



Carmen Li (Faculty of Physics, University of Warsaw, Poland; and School of Computing and Communications, InfoLab21, Lancaster University, Lancaster, United Kingdom)

James Lucietti (School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Scotland, United Kingdom)


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