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Maxwell perturbations on Kerr-anti-de Sitter: quasinormal modes, superradiant instabilities and vector clouds

Scalar and gravitational perturbations on Kerr-anti-de Sitter (Kerr-AdS) black holes have been addressed in the literature and have been shown to exhibit a rich phenomenology. In this paper we complete the analysis of bosonic fields on this background by studying Maxwell perturbations, focusing on superradiant instabilities and vector clouds. For this purpose, we solve the Teukolsky equations numerically, imposing the boundary conditions we have proposed in\cite{Wang:2015goa} for the radial Teukolsky equation. As found therein, two Robin boundary conditions can be imposed for Maxwell fields on Kerr-AdS black holes, one of which produces a new set of quasinormal modes even for Schwarzschild-AdS black holes. Here, we show these different boundary conditions produce two different sets of superradiant modes. Interestingly the "new modes" may be unstable in a larger parameter space. We then study stationary Maxwell clouds, that exist at the threshold of the superradiant instability, with the two Robin boundary conditions. These clouds, obtained at the linear level, indicate the existence of a new family of black hole solutions at the nonlinear level, within the Einstein-Maxwell-AdS system, branching off from the Kerr-Newman-AdS family. As a comparison with the Maxwell clouds, scalar clouds on Kerr-AdS black holes are also studied, and it is shown there are Kerr-AdS black holes that are stable against scalar, but not vector modes, with the same "quantum numbers".