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

Understand

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.