A ug 2 00 9 Isometry - preserving boundary conditions in the Kerr / CFT correspondence

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) × 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 discussed. 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 are well-defined and non-vanishing, but form a centreless Virasoro algebra.