Towards the black hole uniqueness: transverse deformations of the extremal Reissner-Nordstr\"{o}m-(A)dS horizon

TL;DR

This paper investigates possible transverse deformations of extremal Reissner-Nordström-(A)dS horizons, finding that generic charges admit only symmetric deformations, while special charges allow a limited set of non-symmetric deformations.

Contribution

It characterizes all transverse deformations of extremal Reissner-Nordström-(A)dS horizons without symmetry assumptions, revealing charge-dependent constraints on deformation space.

Findings

Generic charge deformations are spherically symmetric.

Fine-tuned charges admit a finite-dimensional deformation space.

No non-symmetric deformations occur for generic charges.

Abstract

We study all transverse deformations of the extremal Reissner-Nordstr\"{o}m-(A)dS horizon in the Einstein-Maxwell theory. No symmetry assumptions are needed. It is shown that for the generic values of the charge, the only allowed deformation is spherically symmetric. However, it is shown that for fine-tuned values of a charge, the space of deformations is larger, yet still finite-dimensional.