Charged scalar perturbations on charged black holes in dRGT massive gravity

TL;DR

This paper investigates the behavior of charged scalar fields around charged black holes in dRGT massive gravity, revealing superradiant instabilities in de Sitter cases and diffusive quasinormal modes influenced by the massive gravity parameter.

Contribution

It provides the first detailed numerical and analytical analysis of quasinormal modes of charged scalar perturbations in dRGT black holes, highlighting effects of the linear term in the metric.

Findings

Unstable modes found for $ ext{l}=0$ in dS black holes with superradiant frequencies.

Stable behavior observed for $ ext{l}=2$ in dS black holes.

Unstable modes with superradiant frequencies also found in AdS black holes.

Abstract

We explore the quasi-stationary profile of massive charged scalar field in a class of charged black hole in dRGT massive gravity. We discuss how the linear term in the metric which is a unique character of the dRGT massive gravity affects structure of the spacetime. Numerical calculations of the quasinormal modes are performed for the charged scalar field in the dRGT black hole background. For asymptotically de Sitter (dS) black hole, an improved asymptotic iteration method is used to obtain the associated quasinormal frequencies. The unstable modes are found for $\ell=0$ case and their corresponding real parts satisfy superradiant condition. For $\ell=2$, the results show that all the de Sitter black holes considered here are stable against a small perturbation. For asymptotically dRGT anti de Sitter (AdS) black hole, unstable modes are found with the frequency satisfying superradiant condition. Effects of massive gravity parameter are discussed. Analytic calculation reveals unique diffusive nature of quasinormal modes in the massive gravity model with the linear term. Numerical results confirm existence of the characteristic diffusive modes in both dS and AdS cases.