QNMs of scalar fields on small Reissner-Nordstr\"{o}m-AdS$\mathbf{_5}$ black holes

TL;DR

This paper investigates the quasinormal modes of charged scalar fields around small Reissner-Nordström-AdS_5 black holes, revealing instabilities at high scalar charges through analytical and numerical methods.

Contribution

It introduces the isomonodromic method to analyze QNMs in small RN-AdS_5 black holes and derives a low-temperature expansion of the fundamental QNM frequency.

Findings

Instabilities occur for large scalar charges in small black holes.

Low-temperature expansion of QNM frequencies is derived.

Numerical evidence supports the presence of instabilities.

Abstract

We study the quasinormal modes (QNMs) of a charged scalar field on a Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS$_{5}$) black hole in the small radius limit by using the isomonodromic method. We also derive the low-temperature expansion of the fundamental QNM frequency. Finally, we provide numerical evidence that instabilities appear in the small radius limit for large values of the charge of the scalar field.