Quasi-normal Modes of Electromagnetic Perturbations of Four-Dimensional Topological Black Holes with Scalar Hair

TL;DR

This paper investigates the electromagnetic perturbations of four-dimensional topological black holes with scalar hair, analyzing their quasi-normal modes both analytically and numerically, and discovering a phase transition in small black holes.

Contribution

It provides the first combined analytical and numerical analysis of electromagnetic quasi-normal modes for these black holes, revealing a second-order phase transition.

Findings

Identification of quasi-normal modes through analytical and numerical methods

Evidence of a second-order phase transition in small black holes

Characterization of electromagnetic perturbations in topological black holes with scalar hair

Abstract

We study the perturbative behaviour of topological black holes with scalar hair. We calculate both analytically and numerically the quasi-normal modes of the electromagnetic perturbations. In the case of small black holes we find evidence of a second-order phase transition of a topological black hole to a hairy configuration.