Superradiance and instability of small rotating charged AdS black holes in all dimensions

TL;DR

This paper extends the analytic understanding of superradiant instability in small rotating charged AdS black holes from four dimensions to all higher dimensions, providing a universal formula for the instability's damping parameter.

Contribution

It offers a complete analytic description of superradiant instability for slowly rotating charged AdS black holes in all dimensions, generalizing previous four-dimensional results.

Findings

Derived the complex frequency spectrum of quasinormal modes.

Obtained a universal analytic expression for the damping parameter.

Showed the real part of the damping parameter describes the superradiant instability universally.

Abstract

Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that the orbital quantum number $ \ell $ can be thought of as an approximate integer. Thus, we obtain the complete low-frequency solution that allows us to calculate the complex frequency spectrum of quasinormal modes, whose imaginary part is determined by a small damping parameter. Finally, we find a remarkably instructive expression for the damping parameter, which appears to be a complex quantity in general. We show that the real part of the damping parameter can be used to give a {\it universal} analytic description of the superradiant instability for slowly rotating charged AdS black holes in all spacetime dimensions.