Critical behaviors of a black hole in an asymptotically safe gravity with cosmological constant

We study the P−V/r₊ criticality and phase transition of a quantum-corrected black hole in asymptotic safety (AS) gravity in the extended phase space. For a black hole, the cosmological constant is dependent on the momentum cutoff or energy scale; therefore, one can naturally treat it as a variable and connect it with thermodynamic pressure. We find that for a quantum-corrected black hole there is a first-order phase transition similar to that of the van der Waals liquid–gas system. We also analyze the types of phase transition between the smaller and larger black hole phases according to Ehrenfest's classification. It is shown that they are second-order phase transitions. (paper)