Phase Transitions of the BTZ Black Hole in New Massive Gravity

Yun Soo Myung

doi:10.1155/2015/478273

Abstract

We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. Form2l2>1/2withm2being the mass parameter of fourth-order terms andl2AdS3curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. Form2l2<1/2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.

Highlights

A black hole could be rendered thermodynamically stable by placing it in four-dimensional anti-de Sitter (AdS4) spacetimes because AdS4 spacetimes play the role of a confining box
It is a natural question to ask how a stable black hole with positive heat capacity could emerge from thermal radiation through a phase transition
We propose that the thermodynamic stability is determined by the sign of the heat capacity while the phase transition is mainly determined by the sign of the free energy

Summary

Introduction

A black hole could be rendered thermodynamically stable by placing it in four-dimensional anti-de Sitter (AdS4) spacetimes because AdS4 spacetimes play the role of a confining box. In order to study the HP phase transition in Einstein gravity, we need to know the Arnowitt-Deser-Misner (ADM) mass [4], the Hawking temperature, and the BekensteinHawking (BH) entropy. These are combined to give the onshell free energy in canonical ensemble which determines the global thermodynamic stability. It implies a deep connection between thermodynamic instability and classical instability for the BTZ black hole only for the new massive gravity [15] It suggests that the phase transition for m2l < 1/2 is quite different from that of m2l > 1/2 case. We wish to explore the presumed phase transition and it will be compared with the Hawking-Page phase transition for m2l > 1/2 case

Thermodynamics of the BTZ Black Hole

Phase Transitions

Discussions