Large Diffeomorphisms and Accidental Symmetry of the Extremal Horizon

TL;DR

The paper identifies an unexpected large diffeomorphism symmetry in the linearized Einstein equations near extremal horizons, expanding the known isometries and linking it to on-shell symmetries in AdS2 and JT gravity.

Contribution

It reveals an accidental symmetry of Einstein equations near extremal horizons, extending the set of solution-mapping transformations beyond known isometries.

Findings

Discovery of a new on-shell large diffeomorphism symmetry.

Extension of symmetry group beyond SL(2) isometries.

Connection to on-shell symmetries in AdS2 and JT gravity.

Abstract

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.