Near-horizon symmetries of extremal black holes

TL;DR

This paper proves the existence of near-horizon SO(2,1) symmetry for extremal black holes in general theories, including higher-derivative corrections, and explores their analytic continuation to SU(2) symmetry solutions.

Contribution

It establishes the universal presence of near-horizon SO(2,1) symmetry for extremal black holes with multiple rotational symmetries in broad gravity theories.

Findings

Proven symmetry for extremal black holes with multiple rotations.

Extended symmetry proof to theories with higher-derivative corrections.

Linked near-horizon solutions to non-extremal solutions via analytic continuation.

Abstract

Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2,1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2,1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers-Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers-Perry solution.