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We study all transverse deformations of the extremalReissner-Nordstr\"{o}m-(A)dS horizon in the Einstein-Maxwell theory. Nosymmetry assumptions are needed. It is shown that for the generic values of thecharge, the only allowed deformation is spherically symmetric. However, it isshown that for fine-tuned values of a charge, the space of deformations islarger, yet still finite-dimensional.

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