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

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 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. * hasan.elmoumni@edu.uca.ma

Phase transition of AdS black hole in massive gravity revisited via new prescription

“…In this framework, the cosmological constant is regarded as thermodynamic pressure and the black hole mass is identified to the enthalpy. Within these peculiar developments, a beautiful and deep analogy between AdS black holes and van der Waals liquid-gas system has been revealed [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] opening a new window towards our understanding of strong gravity and black holes physics.…”

“…Hence, the massive gravities and graviton can help to shed light on the foreseen quantum behavior of gravity [33,34]. Nowadays many approaches have been raised to probe the black hole phase transitions, ranging from the thermodynamics technics via the localisation of discontinuities of the heat capacity [7][8][9][10], thermodynamics geometries by the singularities of their Ricci scalars [11,12], the AdS/CFT tools including entanglement entropy and two-point correlation function [13][14][15][16]35], to quasinormal modes [17][18][19] and chaos structure [31].…”