Large Diffeomorphisms and Accidental Symmetry of the Extremal Horizon

We uncover a symmetry of the linear Einstein equations near extremal horizons. Specifically, acting with a spherically symmetric linearized diffeomorphism on the perturbative solutions to the Einstein-Maxwell equations in the Bertotti-Robinson background, but not acting on the background itself, we find that there is a subset of such transformations under which the equations of motion remain satisfied, with or without additional matter. This represents an "accidental" symmetry in the sense that the set of transformations realizing the mapping among solutions is strictly larger than the ${\rm SL}(2)$ isometries of the background spacetime. We argue that our accidental symmetry can be thought of as an on-shell large diffeomorphism of ${\rm AdS}_2$, which we support in the context of Jackiw-Teitelboim theory.