Superradiant instability of D-dimensional Reissner-Nordstr\"{o}m black hole mirror system

TL;DR

This paper analytically investigates the superradiant instability of a charged scalar field around D-dimensional Reissner-Nordström black holes with a mirror boundary, revealing conditions for instability through quasinormal mode analysis.

Contribution

The study derives analytical expressions for quasinormal frequencies indicating instability, extending understanding of superradiance in higher-dimensional charged black holes with mirror boundaries.

Findings

Charged scalar field is unstable in D-dimensional RN black hole with mirror.

Positive imaginary parts of quasinormal frequencies indicate superradiant instability.

Analytical method used complements numerical approaches for future studies.

Abstract

We analytically study the superradiant instability of a charged massless scalar field in the background of D-dimensional Reissner-Nordstr\"{o}m (RN) black hole caused by the mirror's boundary condition. By using the asymptotic matching method to solve the Klein-Gordon equation that govern the dynamics of the scalar field, we have derived the expressions of the complex parts of the boxed quasinormal frequencies, and shown they are positive in the regime of superradiance. This indicates the charged scalar field is unstable in D-dimensional Reissner-Nordstr\"{o}m (RN) black hole surrounded by mirror. The numerical work to calculate the boxed quasinormal frequencies in this system is still required in the future.