Analytical study of superradiant instability for five-dimensional Kerr-G\"{o}del black hole

TL;DR

This paper analytically investigates the superradiant instability of five-dimensional Kerr-G"{o}del black holes, revealing that scalar perturbations grow over time due to boundary conditions similar to those in AdS spacetime.

Contribution

It provides an analytical demonstration of superradiant instability in five-dimensional Kerr-G"{o}del black holes using matched asymptotic expansions, a novel approach for this spacetime.

Findings

Superradiant modes are unstable with positive imaginary parts of quasinormal frequencies.

Instability arises due to Dirichlet boundary conditions at infinity, akin to AdS black holes.

The study confirms the presence of growing scalar perturbations in this spacetime.

Abstract

We present an analytical study of superradiant instability of rotating asymptotically G\"{o}del black hole (Kerr-G\"{o}del black hole) in five-dimensional minimal supergravity theory. By employing the matched asymptotic expansion method to solve Klein-Gordon equation of scalar field perturbation, we show that the complex parts of quasinormal frequencies are positive in the regime of superradiance. This implies the growing instability of superradiant modes. The reason for this kind of instability is the Dirichlet boundary condition at asymptotic infinity, which is similar to that of rotating black holes in anti-de Sitter (AdS) spacetime.