Non-linear charged AdS black hole in massive gravity

Cao H Nam

doi:10.1140/epjc/s10052-018-6498-1

Abstract

In the context of the non-linear electrodynamics and the Einstein-massive gravity, we have obtained a 4hbox {D} non-linear charged AdS black hole solution. Then, we investigated its horizon structure. In addition, the thermodynamics and phase structure of this black hole solution have been studied in details. We have computed various thermodynamic quantities of the black hole, such as the temperature, entropy, the heat capacity at constant pressure, or the Gibbs free energy. The black hole can undergo the first-order, second-order phase transitions which depend crucially on the effective horizon curvature, the sign of the coupling parameter c_1, the characteristic parameter of the non-linear electrodynamics, as well as the pressure. Finally, we derived the equation of state and studied P-V criticality in the case of the positive effective horizon curvature.

Highlights

anti-de Sitter (AdS) (RN-AdS) black hole can undergo a first-order phase transition which is similar to the liquid–gas phase transition [11,12]
We have derived a solution of 4D non-linear charged AdS black hole, which is spherically-symmetric and static, in the context of the non-linear electrodynamics and the Einstein-massive gravity
The non-linear electrodynamics is characterized by a fixed parameter k by which the charge Q and the mass M of the system are related as, Q2 = Mk

Summary

Introduction

AdS (RN-AdS) black hole can undergo a first-order phase transition which is similar to the liquid–gas phase transition [11,12]. In 2000, Ayon-Beato and Garcia reobtained the Bardeen black hole as a gravitational collapse of some magnetic monopole, in the scenario of Einstein gravity coupled to the non-linear electrodynamics [63]. Because the non-linear electrodynamics can lead to the regular black hole solutions, it has received many recent studies [19,33,39,64–85]. (Note that, any other combination of hμν hμν and h2 would lead to the appearance of the Boulware-Deser ghost [88]) This theory is well-known as the linear massive gravity theory. With the progress in the understanding of the massive gravity, various black hole solutions and their thermodynamics have been extensively studied in the presence of the graviton mass [32,95–109]. In this paper, inspired by the nonlinear electrodynamics, we would like to study the charged AdS black hole with the non-linear source in Einstein-dRGT gravity.

The black hole solution

H cc1r H 2

Thermodynamics and phase transitions

Conclusion