Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity

Ming Zhang,De-Cheng Zou,Rui-Hong Yue

doi:10.1155/2017/3819246

Ming Zhang, De-Cheng Zou + Show 1 more

Open Access

https://doi.org/10.1155/2017/3819246

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Abstract

Motivated by recent developments of black hole thermodynamics in de Rham, Gabadadze, and Tolley (dRGT) massive gravity, we study the critical behaviors of topological Anti-de Sitter (AdS) black holes in the presence of Born-Infeld nonlinear electrodynamics. Here the cosmological constant appears as a dynamical pressure of the system and its corresponding conjugate quantity is interpreted as thermodynamic volume. This shows that, besides the Van der Waals-like SBH/LBH phase transitions, the so-called reentrant phase transition (RPT) appears in four-dimensional space-time when the coupling coefficients cim2 of massive potential and Born-Infeld parameter b satisfy some certain conditions. In addition, we also find the triple critical points and the small/intermediate/large black hole phase transitions for d=5.

Highlights

Einstein’s General Relativity (GR), which describes that the graviton is a massless spin-2 particle, helped us to understand the dynamics of the Universe [1,2,3]
One of the alternating theories of gravity is known as a massive gravity, where mass terms are added to the GR action
In the extended phase space, we have studied the phase transition and critical behavior of topological Anti-de Sitter (AdS) black holes in the four- and five-dimensional Born-Infeld-massive gravity

Summary

Introduction

Einstein’s General Relativity (GR), which describes that the graviton is a massless spin-2 particle, helped us to understand the dynamics of the Universe [1,2,3]. Vainshtein [10] proposed that the linear massive gravity can be recovered to GR through the “Vainshtein Mechanism” at small scales by including nonlinear terms in the massive gravity action It usually brings various instabilities for the gravitational theories on the nonlinear level by adding generic mass terms, since this model suffers from a pathology called a “Boulware-Deser” (BD) ghost. Some investigations for thermodynamics of AdS black holes have been generalized to the extended phase space in the dRGT massive gravity [47,48,49,50], which show the Van der Waals-like SBH/LBH phase transition in the charged topological AdS black holes. We will generalize the discussion to topological AdS black holes for d = 4 and 5 in the Born-Infeld-massive gravity.

Thermodynamics of d-Dimensional Born-Infeld AdS Black Holes

Conclusions and Discussions