Critical phenomena of regular black holes in anti-de Sitter space-time

TL;DR

This paper investigates the thermodynamic critical phenomena of regular black holes in anti-de Sitter space, revealing deviations from classical Van der Waals behavior and exploring their unique phase transition properties.

Contribution

It introduces a new regular black hole solution in AdS space coupled with non-linear electrodynamics and analyzes its distinct critical phenomena and thermodynamic behavior.

Findings

Violation of Maxwell's equal area law in the $P-V$ diagram

Critical point does not coincide with the inflection point of isotherms

Heat capacity remains finite at the critical point

Abstract

In General Relativity coupled to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward-AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black hole solution. We further discuss its thermodynamic properties and study the critical phenomena in the extended phase space where the cosmological constant is treated as a thermodynamic variable as well as the parameter associated with the non-linear electrodynamics. We obtain many interesting results such as: the Maxwell's equal area law in the $P-V$ (or $S-T$) diagram is violated and consequently the critical point $(T_*\,,P_*)$ of the first order small-large black hole transition does not coincide with the inflection point ($T_c\,,P_c$) of the isotherms; the Clapeyron equation describing the coexistence curve of the Van der Waals (vdW) fluid is no longer valid; the heat capacity at constant pressure is finite at the critical point; the various exponents near the critical point are also different from those of the vdW fluid.