Anti-de-Sitter-Maxwell-Yang-Mills Black Holes Thermodynamics from Nonlocal Observables Point of View

H El Moumni

doi:10.1155/2019/6870793

Abstract

In this paper we analyze the thermodynamic properties of the Anti-de-Sitter black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many approaches and in different thermodynamical ensembles (canonical/grand canonical). First, we give a concise overview of this phase structure in the entropy-thermal diagram for fixed charges and then we investigate this thermodynamical structure in fixed potentials ensemble. The next relevant step is recalling the nonlocal observables such as holographic entanglement entropy and two-point correlation function to show that both observables exhibit a Van der Waals-like behavior in our numerical accuracy and just near the critical line as the case of the thermal entropy for fixed charges by checking Maxwell’s equal area law and the critical exponent. In the light of the grand canonical ensemble, we also find a newly phase structure for such a black hole where the critical behavior disappears in the thermal picture as well as in the holographic one.

Highlights

A great emphasis has been put on the application of the Anti-de-Sitter/conformal field theory correspondence [1, 2] which plays a pivotal role in recent developments of many physical themes [3,4,5]; in this particular context the thermodynamics of Anti-de-Sitter black holes become more attractive for investigation [6]
This work is organized as follow: First, we present some thermodynamic properties and phase structure of the Einstein-Maxwell-Yang-MillsAdS gravity (EMYM)-AdS black holes in-plane in canonical and grand canonical ensemble
In this work We have investigated the phase transition of Anti-de-Sitter black hole in the Einstein-Maxwell-Yang-Mills gravity considering the canonical and the grand canonical ensemble

Summary

Introduction

A great emphasis has been put on the application of the Anti-de-Sitter/conformal field theory correspondence [1, 2] which plays a pivotal role in recent developments of many physical themes [3,4,5]; in this particular context the thermodynamics of Anti-de-Sitter black holes become more attractive for investigation [6].In general, black hole thermodynamics has emerged as a fascinating laboratory for testing the predictions of candidate theories of quantum gravity. Having obtained the phase picture of the thermal entropy of the AdS-Maxwell-Yang-Mills black hole, the canonical/grand canonical ensemble, we will revisit the phase structure of the entanglement entropy and two-point correlation function to see whether they have similar phase structure in each thermodynamical ensemble.

Results

Conclusion