Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

Abstract

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 [1] 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 KerrNewman-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".

Kerr black holes with Proca hair

“…It remains as an open question if the same could be achieved with a single real Proca field, especially in view of the result in [77], since such real Proca field already has two independent modes.…”

Photonic black resonators and photon stars in AdS5

“…1 For Kerr-AdS 4 , the Maxwell superradiant instability is shown in Ref. [26]. In MPAdS 5 , we will study it in section 2.…”

Superradiance of a global monopole in Reissner–Nordström(–AdS) space-time

“…This observation is also present in rotating and/or charged [35,[54][55][56][57] AdS black holes in higher dimensions. Moreover, gravitational or Maxwell perturbations may also trigger superradiance instability for AdS black holes [58][59][60][61]. This instability causes the black hole to loose some of its angular momentum and horizon charge.…”