P-V criticality of conformal anomaly corrected AdS black holes

TL;DR

This paper explores how conformal anomaly affects the thermodynamic phase transitions of AdS black holes, revealing that it influences critical quantities and the existence of physical critical points.

Contribution

It extends the study of $P$-$V$ criticality in AdS black holes by analyzing the impact of conformal anomaly on both charged and uncharged cases, highlighting new dependencies.

Findings

Conformal anomaly does not affect Van der Waals critical behavior in uncharged black holes.

In charged black holes, conformal anomaly alters critical quantities and the ratio $rac{P_c v_c}{T_c}$.

A specific range of the conformal parameter ensures the existence of physically meaningful critical points.

Abstract

The effects of conformal anomaly on the thermodynamics of black holes are investigated in this Letter from the perspective of $P-V$ criticality of AdS black holes. Treating the cosmological constant as thermodynamic pressure, we extend the recent research to the extended phase space. Firstly, we study the $P$-$V$ criticality of the uncharged AdS black holes with conformal anomaly and find that conformal anomaly does not influence whether there exists Van der Waals like critical behavior. Secondly, we investigate the $P$-$V$ criticality of the charged cases and find that conformal anomaly influences not only the critical physical quantities but also the ratio $\frac{P_cr_c}{T_c}$. The ratio is no longer a constant as before but a function of conformal anomaly parameter $\tilde{\alpha}$. We also show that the conformal parameter should satisfy a certain range to guarantee the existence of critical point that has physical meaning. Our results show the effects of conformal anomaly.