Phase Transitions in Charged Topological-AdS Black Holes

TL;DR

This paper investigates the stability and phase transition behavior of charged topological-AdS black holes by analyzing their quasi-normal modes and identifying a second-order phase transition at a critical temperature.

Contribution

It provides analytical and numerical calculations of quasi-normal modes and reveals a second-order phase transition with unique dissipative mode behavior at the critical point.

Findings

Identification of a second-order phase transition at a critical temperature

Behavior of dissipative modes becomes singular at the critical point

Analytical and numerical methods complement each other in the study

Abstract

We study the perturbative behaviour of charged topological-AdS black holes. We calculate both analytically and numerically the quasi-normal modes of the electromagnetic and gravitational perturbations. Keeping the charge-to-mass ratio constant, we show that there is a second-order phase transition at a critical temperature at which the mass of the black hole vanishes. We pay special attention to the purely dissipative modes appearing in the spectrum as they behave singularly at the critical point.