Critical behaviors of black holes in the Einstein-Maxwell gravity with conformal anomaly

TL;DR

This paper investigates the phase transition behavior of 4D AdS black holes in Einstein-Maxwell gravity with conformal anomaly, revealing conditions for Van der Waals-like transitions and critical exponents matching classical fluids.

Contribution

It introduces the analysis of $P-V$ criticality in Einstein-Maxwell black holes with conformal anomaly, identifying specific conditions for phase transitions and calculating critical exponents.

Findings

No phase transition for $k=0$ or -1.

Van der Waals-like phase transition occurs under certain charge and anomaly coefficient conditions.

Critical exponents match those of classical Van der Waals fluids.

Abstract

We study $P-V$ critical behavior of 4-dimensional AdS black hole in the Einstein-Maxwell gravity with conformal anomaly by treating the cosmological constant as a variable related to the thermodynamic pressure. It shows that there is no phase transition if taking $k=0$ or -1. When the charge $q_1$ of conformal field and the coefficient $\alpha$ satisfy a certain relation, the Van der Waal like phase transition for the spherical black hole can occur in case of the temperature is lower than the small critical temperature or higher than the large one. We also evaluate the critical exponents of the phase transitions and find that the thermodynamic exponents associated with this 4-dimensional AdS black hole coincide with those of the van der Waals fluid.