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

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.