Quasinormal modes and stability of boosted Reissner-Nordstr\"om AdS black holes

TL;DR

This paper studies the stability of small-acceleration boosted Reissner-Nordström AdS black holes against scalar perturbations by analyzing quasinormal modes, revealing stability and a fine-structure in the mode spectrum.

Contribution

It introduces a numerical analysis of scalar perturbations on accelerated AdS black holes, highlighting the existence of fine-structure in quasinormal modes not seen in non-accelerated cases.

Findings

Black holes are stable against scalar perturbations.

Existence of fine-structure in quasinormal mode spectrum.

Modes show both damped and purely imaginary oscillations.

Abstract

We investigate the numerical stability of accelerated AdS black holes against linear scalar perturbations. In particular, we study the evolution of a probe non-minimally coupled scalar field on Schwarzschild and Reissner-Nordstr\"om AdS black holes with small accelerations by computing the quasinormal modes of the perturbation spectrum. We decompose the scalar field Klein-Gordon equation and study the eigenvalue problem for its angular and radial-temporal parts using different numerical methods. The angular part is written in terms of the Heun solution and expanded through the Frobenius method which turns out to give eigenvalues qualitatively similar to the ones obtained through the spherical harmonics representation. The radial-temporal evolution renders a stable field profile which is decomposed in terms of damped and purely imaginary oscillations of the quasinormal modes. We calculate the respective frequencies for different spacetime parameters showing the existence of a fine-structure in the modes, for both real and imaginary parts, which is not present in the non-accelerated AdS black holes. Our results indicate that the Schwarzschild and Reissner-Nordstr\"om AdS black holes with small accelerations are stable against linear scalar perturbations.