ÃÛÌÒTV

Black holes in anti-de Sitter (AdS) backgrounds play a pivotal role in the gauge/gravity duality where they determine, among other things, the approach to equilibrium of the dual field theory. We undertake a detailed analysis of perturbed Kerr-AdS black holes, including the computation of its quasinormal modes, hydrodynamic modes and superradiantly unstable modes. For that we solve the Teukolsky master equation using the associated spin-weighted spheroidal harmonic decomposition subject to boundary conditions (BCs) that are asymptotically global AdS. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. Our results shed light on the possibility of new black hole phases with a single Killing field, possible new holographic phenomena and phases in the presence of a rotating chemical potential, and close a crucial gap in our understanding of linearized perturbations of black holes in AdS scenarios.