Superradiance and black hole bomb in five-dimensional minimal ungauged supergravity

TL;DR

This paper analytically investigates superradiant instability in a five-dimensional black hole bomb model within minimal ungauged supergravity, revealing that scalar perturbations grow exponentially, indicating instability.

Contribution

It provides an analytical solution for quasinormal modes in a five-dimensional black hole bomb, demonstrating superradiant instability in this specific supergravity context.

Findings

All scalar modes undergo negative damping in superradiance regime

Scalar perturbations exhibit exponential growth, confirming instability

Analytical frequency spectrum derived for near-horizon and far regions

Abstract

We examine the black hole bomb model which consists of a rotating black hole of five-dimenensional minimal ungauged supergravity and a reflecting mirror around it. For low-frequency scalar perturbations, we find solutions to the Klein-Gordon equation in the near-horizon and far regions of the black hole spacetime. To avoid solutions with logarithmic terms, we assume that the orbital quantum number $ l $ takes on nearly, but not exactly, integer values and perform the matching of these solutions in an intermediate region. This allows us to calculate analytically the frequency spectrum of quasinormal modes, taking the limits as $ l $ approaches even or odd integers separately. We find that all $ l $ modes of scalar perturbations undergo negative damping in the regime of superradiance, resulting in exponential growth of their amplitudes. Thus, the model under consideration would exhibit the superradiant instability, eventually behaving as a black hole bomb in five dimensions.