Anti-de-Sitter-Maxwell-Yang-Mills black holes thermodynamics from nonlocal observables point of view

TL;DR

This paper explores the thermodynamics of Anti-de Sitter black holes in Einstein-Maxwell-Yang-Mills gravity using nonlocal observables like holographic entanglement entropy, revealing Van der Waals-like behavior and new phase structures.

Contribution

It demonstrates the application of nonlocal observables to analyze black hole phase transitions and uncovers novel phase behavior in grand canonical ensembles.

Findings

Nonlocal observables show Van der Waals-like behavior near critical points.

A new phase structure emerges in grand canonical ensemble where critical behavior vanishes.

Holographic entanglement entropy and two-point functions reflect thermodynamic phase transitions.

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.