The description of phase transition in a black hole with conformal anomaly in the Ehrenfest's scheme

TL;DR

This paper investigates the phase transition behavior of black holes with conformal anomaly using Ehrenfest's scheme, concluding that they undergo second order phase transitions, unlike black holes without conformal anomaly.

Contribution

It applies Ehrenfest's equations to analyze black hole phase transitions with conformal anomaly, establishing the second order nature of these transitions and contrasting with black holes lacking anomaly.

Findings

First order phase transition is absent in conformal anomaly black holes.

Black holes with conformal anomaly exhibit second order phase transitions.

Black holes without conformal anomaly do not undergo second order phase transitions.

Abstract

We make use of the Ehrenfest's equation to explore the phase transition of a black hole with conformal anomaly. The first order phase transition is ruled out because no discontinuity appears in entropy of the black holes. We find that the phase transition of black holes belong to the second order subject to the Ehrenfest's equations. Further we also show that the second order phase transition will not happen for the black holes without conformal anomaly.