Near Horizon Structure of Extremal Vanishing Horizon Black Holes

TL;DR

This paper analyzes the near horizon structure of extremal vanishing horizon black holes, revealing a universal 3D maximally symmetric subspace and extending results to near-EVH cases, with implications for supergravity and holography.

Contribution

It provides the most general near horizon ansatz for EVH black holes and proves the universal presence of a 3D maximally symmetric space under broad conditions.

Findings

Near horizon EVH geometry has a 3D maximally symmetric subspace.

Matter fields satisfying strong energy condition lead to AdS3 or flat space.

Results extend to near-EVH black holes with BTZ geometry.

Abstract

We study the near horizon structure of Extremal Vanishing Horizon (EVH) black holes, extremal black holes with vanishing horizon area with a vanishing one-cycle on the horizon. We construct the most general near horizon EVH and near-EVH ansatz for the metric and other fields, like dilaton and gauge fields which may be present in the theory. We prove that (1) the near horizon EVH geometry for generic gravity theory in generic dimension has a three dimensional maximally symmetric subspace; (2) if the matter fields of the theory satisfy strong energy condition either this 3d part is AdS$_3$, or the solution is a direct product of a locally 3d flat space and a $d-3$ dimensional part; (3) these results extend to the near horizon geometry of near-EVH black holes, for which the AdS$_3$ part is replaced with BTZ geometry. We present some specific near horizon EVH geometries in 3, 4 and 5 dimensions for which there is a classification. We also briefly discuss implications of these generic results for generic (gauged) supergravity theories and also for the thermodynamics of near-EVH black holes and the EVH/CFT proposal.