Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity

Yunqi Liu,De-Cheng Zou,Ruihong Yue

doi:10.1140/epjc/s10052-017-4937-z

Abstract

In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of charged topological Anti-de Sitter (AdS) black holes in four-dimensional massive gravity. We find that the signature of this SBH/LBH phase transition is detected in the isobaric as well as in the isothermal process. This further supports the idea that the QNMs can be an efficient tool to investigate the thermodynamical phase transition.

Highlights

The thermodynamical phase transition of a black hole is always a hot topic in black hole physics
A particular emphasis has been put on the study of the black hole phase transitions in Anti-de Sitter (AdS) spacetime in Ref. [39], which asserted the analogy between the Van der Waals liquid–gas system behavior and the charged AdS black hole
Previous thermodynamical discussions for Reissner–Nordstrom–Anti de Sitter (RN-AdS) black holes show that the Van der Waals-like SBH/LBH only occurs for spherical horizon topology k = 1

Summary

Introduction

The thermodynamical phase transition of a black hole is always a hot topic in black hole physics. In the extended phase space, we have recovered the deep relation between the dynamical perturbation and the Van der Waals-like SBH/LBH phase transition in the fourdimensional Reissner–Nordstrom–Anti de Sitter (RN-AdS) black holes with spherical horizon (k = 1) [97]. It is necessary to point out that in four-dimensional dRGT massive gravity, there always exists a so-called Van der Waals-like SBH/LBH phase transition for the charged AdS black holes when the horizon topology is spherical (k = 1), Ricci flat (k = 0) or hyperbolic (k = −1) [71]. This phenomenon rarely occurs, since this Van der Waals-like SBH/LBH phase transition was usually recovered in a variety of spherical horizon black hole backgrounds Motivated by these results, in this paper we find it crucial and well justified to reconsider the charged topological AdS black hole in four-dimensional dRGT massive gravity.

Phase transition of charged topological AdS black hole in massive gravity

Perturbations of charged topological AdS black hole in massive gravity

Isobaric phase transition

Isothermal phase transition

Findings

Conclusions and discussions