Instability and phase transitions of a rotating black hole in the presence of perfect fluid dark matter

Seyed Hossein Hendi,Azadeh Nemati,Mubasher Jamil,Kai Lin

doi:10.1140/epjc/s10052-020-7829-6

Abstract

In this paper, we study the thermodynamic features of a rotating black hole surrounded by perfect fluid dark matter. We analyze the critical behavior of the black hole by considering the known relationship between pressure and cosmological constant. We show that the black hole admits a first order phase transition and, both rotation and perfect fluid dark matter parameters have a significant impact on the critical quantities. We also introduce a new ad hoc pressure related to the perfect fluid dark matter and find a first order van der Waals like phase transition. In addition, using the sixth order WKB method, we investigate the massless scalar quasinormal modes (QNMs) for the static spherically symmetric black hole surrounded by dark matter. Using the finite difference scheme, the dynamical evolution of the QNMs is also discussed for different values of angular momentum and overtone parameters.

Highlights

anti-de Sitter (AdS) black holes [3,4]
They suggested that the changes of the photon sphere radius and the minimum impact parameter can serve as order parameters for a small-large black hole phase transition
We considered the Kerr–AdS black hole surrounded by the perfect fluid dark matter (PFDM)

Summary

Introduction

AdS black holes [3,4]. This phase transition is identified with the liquid–gas phase transition of the van der Waals fluid [5]. It is shown that the characteristic swallow-tail behavior is observed for the definite Rényi entropy parameter, which is corresponding to a small/large black hole phase transition analogous to the picture of rotating black holes in AdS space. It is worth mentioning the possibility of studying the extended phase space from the viewpoint of AdS/CFT correspondence. We are interested to investigate how the presence of perfect fluid dark matter affect the thermodynamical/dynamical aspects of black holes.

Rotating perfect fluid dark matter black hole and its thermodynamics

Phase transitions

Quasi-normal modes of a static PFDM black hole

Findings

Conclusion