Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

TL;DR

This paper investigates the phase structure and critical behavior of charged AdS black holes surrounded by modified Chaplygin gas, revealing van der Waals-like phase transitions and applying geometrothermodynamic tools for analysis.

Contribution

It introduces a novel black hole solution with a surrounding MCG and analyzes its thermodynamic phase transitions using multiple geometrothermodynamic methods.

Findings

Black hole exhibits van der Waals-like small/large phase transition.

Critical exponents indicate universal scaling behavior.

Geometrothermodynamic metrics successfully identify critical points.

Abstract

By considering the concept of the modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and dark matter, we construct a static, spherically charged black hole (BH) solution in the framework of General Relativity. The $P-V$ criticality of the charged anti-de Sitter (AdS) BH with a surrounding MCG is explored in the context of the extended phase space, where the negative cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH phase transition is analogous to the van der Waals liquid/gas phase transition. Accordingly, along the $P-V$ phase spaces, we derive the BH equations of state and then numerically evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities near criticality into a universal class. The use of \emph{geometrothermodynamic} (GT) tools finally offers a new perspective on discovering the critical phase transition point. At this stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings are therefore non-trivial, as each GT class metric captures at least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with surrounding MCG.