Extremal Isolated Horizon/CFT Correspondence

TL;DR

This paper explores the near-horizon geometry of extremal isolated horizons, demonstrating their equivalence to known extremal Kerr metrics and proposing a generalized Kerr/CFT correspondence for non-stationary extremal black holes.

Contribution

It derives the near-horizon limit of extremal isolated horizons in Bondi-like coordinates and extends the Kerr/CFT correspondence to a broader class of extremal black holes.

Findings

Near-horizon geometries of extremal isolated horizons are equivalent to extremal Kerr geometries.

The Kerr/CFT correspondence can be generalized beyond stationary black holes.

Explicit coordinate transformations relate different near-horizon metric forms.

Abstract

The near-horizon limit of the extremal (weakly) isolated horizon is obtained under the Bondi-like coordinates. For the vacuum case, explicit coordinate transformation relating the near-horizon metric under the Bondi-like coordinates and the standard Poincar\'e-type or global near-horizon metric of the extremal Kerr black hole is found, which shows that the two geometries are the same. Combined with the known thermodynamics of the (weakly) isolated horizon, it is argued that the Kerr/CFT correspondence can be generalized to the case of a large class of non-stationary extremal black holes.