Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

TL;DR

This paper analyzes scalar perturbations of slowly accelerating Kerr-Newman-AdS black holes, deriving angular eigenvalues and quasi-normal mode frequencies using isomonodromic deformation methods, contributing to understanding black hole stability.

Contribution

It introduces a novel approach employing isomonodromic deformations to compute scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes.

Findings

Asymptotic expansion for angular eigenvalues in small acceleration and rotation limit

Reformulation of boundary value problem using isomonodromic tau function

Computed quasi-normal mode frequencies for the black holes

Abstract

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.