Critical Behavior of Black Holes in an Einstein–Maxwell Gravity with a Conformal Anomaly

We study the P–V critical behavior of a four-dimensional AdS black hole in an Einstein–Maxwell gravity with a conformal anomaly by treating the cosmological constant as a variable that is related to the thermodynamic pressure. It is shown that there will be no phase transition if k=0 or −1 are taken. When the charge q₁ of the conformal field and the coefficient α satisfy a certain relation, the van de Waals like phase transition for the spherical black hole can occur where 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 four-dimensional AdS black hole coincide with those of the van de Waals fluid.