Superradiant Instability of Five-Dimensional Rotating Charged AdS Black Holes

TL;DR

This paper analytically investigates the superradiant instability of small five-dimensional rotating charged AdS black holes, revealing that only even orbital modes grow exponentially, unlike the four-dimensional case where all modes are unstable.

Contribution

It provides an analytical solution for quasinormal modes of five-dimensional rotating charged AdS black holes, identifying mode-specific superradiant instabilities.

Findings

Only even orbital quantum number modes are unstable and grow exponentially.

Odd modes oscillate with frequency shifts without damping.

Instability behavior differs from four-dimensional Kerr-AdS black holes.

Abstract

We study the instability of small AdS black holes with two independent rotation parameters in minimal five-dimensional gauged supergravity to massless scalar perturbations. We analytically solve the Klein-Gordon equation for low-frequency perturbations in two regions of the spacetime of these black holes: namely, in the region close to the horizon and in the far-region. By matching the solutions in an intermediate region, we calculate the frequency spectrum of quasinormal modes. We show that in the regime of superradiance only the modes of even orbital quantum number undergo negative damping, resulting in exponential growth of the amplitude. That is, the black holes become unstable to these modes. Meanwhile, the modes of odd orbital quantum number do not undergo any damping, oscillating with frequency-shifts. This is in contrast with the case of four-dimensional small Kerr-AdS black holes which exhibit the instability to all modes of scalar perturbations in the regime of superradiance.