Notes on the Hidden Conformal Symmetry in the Near Horizon Geometry of the Kerr Black Hole

TL;DR

This paper explores the hidden conformal symmetry in the near horizon geometry of Kerr black holes, linking it to the Kerr/CFT correspondence and analyzing implications for black hole entropy.

Contribution

It investigates the hidden conformal symmetry in the near horizon limit of Kerr black holes and relates it to asymptotic symmetry and entropy deviations.

Findings

Identifies hidden conformal symmetry in the near horizon region.

Connects the symmetry to the Kerr/CFT correspondence.

Derives entropy deviation from extremality.

Abstract

Toward the Kerr/CFT correspondence for generic non-extremal Kerr black hole, the analysis of scattering amplitudes by near extremal Kerr provides a clue. This pursuit reveals a hidden conformal symmetry in the law frequency wave equation for a scalar field in a certain spacetime region referred to as the near region. For extremal case, the near region is expected to be the near horizon region in which the correspondence via the asymptotic symmetry is studied. We investigate the hidden conformal symmetry in the near horizon limit and consider the relation between the hidden conformal symmetry and the asymptotic symmetry in the near horizon limit. By using an appropriate definition of the quasi-local charge, we obtain the deviation of the entropy from the extremality.