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 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.