Topological AdS black holes surrounded by Chaplygin dark fluid: from stability to geometrothermodynamic analysis

TL;DR

This paper constructs a new higher-dimensional AdS black hole solution with Chaplygin dark fluid, analyzing its thermodynamic phase transitions, stability, and microstructure using geometrothermodynamics, revealing similarities to van der Waals systems.

Contribution

It introduces a novel AdS black hole model with Chaplygin dark fluid and applies advanced thermodynamic and geometric analyses to explore its phase structure and microstructure.

Findings

Black hole phase transitions resemble van der Waals liquid/gas behavior.

Different geometrothermodynamic metrics predict phase transition points.

Critical exponents indicate universal scaling near criticality.

Abstract

Implementing the concept of Dark Fluid with a Chaplygin-like equation of state within General Relativity, we construct a new higher-dimensional, static, and spherically symmetric anti-de Sitter (AdS) black hole solution. Energy conditions are explored alongside curvature singularity tools. The inspection at the level of the phase structure and $P-v$ critical behavior is carried out in the context of the extended phase space, where the cosmological constant appears as pressure. Our findings disclose non-trivial similarities between the small/large phase transition of AdS black holes surrounded by Chaplygin dark fluid and van der Waals systems' liquid/gas phase transition. This analysis offers insights into the physical interpretation of the $P-v$ diagram and identifies critical exponents that reveal the scaling behavior of thermodynamic quantities close to criticality in a universal manner. We finally deepen our understanding of the thermodynamic properties and microstructure of AdS black holes by leveraging the geometrothermodynamic formalism. Specifically, we employ tools, including Weinhold, Ruppeiner, Hendi-Panahiyan-Eslam-Momennia (HPEM) and Quevedo classes I and II. We show that each class of metrics predicts either the physical limitation point and/or the phase-transition critical points, with HPEM and Quevedo formulations providing richer information about the phase transitions. Altogether, this study contributes to advancing our knowledge of the role of Chaplygin gas in General Relativity and thoroughly examining the thermodynamic phase structure of high-dimensional AdS black holes under extreme conditions.