Towards the black hole uniqueness: transverse deformations of the extremal Reissner-Nordström-(A)dS horizon

Abstract

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