Isometry-preserving boundary conditions in the Kerr/CFT correspondence

TL;DR

This paper investigates alternative boundary conditions in the Kerr/CFT correspondence that preserve isometries of extremal Kerr black holes, exploring how these conditions influence the associated Virasoro symmetries and conserved charges.

Contribution

It provides a partial classification of boundary conditions that enhance either SL(2,R) or U(1) isometries to Virasoro algebras in near-horizon geometries of extremal Kerr black holes.

Findings

Boundary conditions can enhance SL(2,R) or U(1) isometries to Virasoro algebras.

Conserved charges form a centreless Virasoro algebra under SL(2,R)-enhancing boundary conditions.

Alternative boundary conditions expand the understanding of Kerr/CFT correspondence symmetry structures.

Abstract

The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) x U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are explored. Partial classifications are provided of the boundary conditions enhancing the SL(2,R) isometries or separately the U(1) isometry to a Virasoro algebra. In the case of SL(2,R)-enhancing boundary conditions of a near-horizon geometry of the type considered, the conserved charges associated to the generators of the asymptotic Virasoro symmetry form a centreless Virasoro algebra.