Critical Phenomena in Higher Curvature Charged AdS Black Holes

Arindam Lala

doi:10.1155/2013/918490

Abstract

In this paper, we have studied the critical phenomena in higher curvature charged AdS black holes. We have considered Lovelock-Born-Infeld-AdS black hole as an example. The thermodynamics of the black hole have been studied which reveals the onset of a higher-order phase transition in the black hole in the canonical ensemble (fixed charge ensemble) framework. We have analytically derived the critical exponents associated with these thermodynamic quantities. We find that our results fit well with the thermodynamic scaling laws and consistent with the mean field theory approximation. The suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface have been derived.

Highlights

Constructing gravity theories in higher dimensions has been an interesting topic of research for the past several decades
In this paper we have analyzed the critical phenomena in higher curvature charged black holes in a canonical framework. For this purpose we have considered the third order Lovelock-Born-Infeld-anti-de Sitter (AdS) (LBI-AdS) black holes in a spherically symmetric space-time
Unlike the AdS black holes in the Einstein gravity, one interesting property of the higher curvature black holes is that the usual area law of entropy does not hold for these black holes

Summary

Introduction

Constructing gravity theories in higher dimensions (i.e., greater than four) has been an interesting topic of research for the past several decades. If we want to study the effect of backreaction of quantum field energy on the laws on black hole mechanics, we are required to consider higher curvature interactions [19] From this point of view it is very much natural to study the effect of higher curvature terms on the thermodynamic properties of black holes. In this paper we have studied the critical phenomena in the third-order LBI-AdS black holes in seven dimensions. Despite having some distinct features in the higher curvature gravity theories, for example, the usual area law valid in Einstein gravity does not hold in these gravity theories, the critical exponents are found to be identical with those in the usual Einstein gravity This result shows that the AdS black holes, studied so far, belong to the same universality class.

Thermodynamic Variables of Higher Curvature Charged AdS Black Holes

Phase Transition and Stability of the Third-Order LBI-AdS Black Hole

Phase III r2

Critical Exponents and Scaling Hypothesis

Conclusions