EVH Black Holes, AdS3 Throats and EVH/CFT Proposal

TL;DR

This paper explores the near horizon geometry of EVH black holes, revealing a connection to AdS3/CFT2 correspondence and proposing a duality with a 2D conformal field theory, extending known extremal black hole results.

Contribution

It demonstrates that EVH black holes develop a pinching AdS3 throat in the near horizon limit and proposes a dual 2D CFT description, extending the EVH/CFT correspondence.

Findings

Near horizon EVH black holes develop a pinching AdS3 throat.

The pinching AdS3 orbifold is resolved by taking G4 to zero while keeping entropy finite.

Evidence supports the EVH/CFT duality and its relation to Kerr/CFT.

Abstract

Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T) and vanishing horizon area Ah, but with finite Ah/T ratio,the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS3. This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS2 throat. We show that in the near EVH near horizon limit the pinching AdS3 factor turns to a pinching BTZ black hole and that this near horizon limit is indeed a decoupling limit. We argue that the pinching AdS3 or BTZ orbifold is resolved if the near horizon limit is accompanied by taking the 4d Newton constant G4 to zero such that the Bekenstein-Hawking entropy S = Ah/(4G4) remains finite. We propose that in this limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of evidence in support of the EVH/CFT correspondence and comment on its connection to the Kerr/CFT proposal and speculations how the EVH/CFT may be used to study generic e.g. Schwarzchild-type black holes.