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

TL;DR

This paper investigates the phase transitions of quantum-corrected black holes in asymptotically safe gravity, revealing van der Waals-like behavior and second-order phase transitions at critical points.

Contribution

It introduces a thermodynamic analysis of black holes with a variable cosmological constant linked to energy scale in asymptotic safety gravity, highlighting phase transition characteristics.

Findings

Black holes exhibit van der Waals-like first-order phase transitions.

Critical points correspond to second-order phase transitions.

Thermodynamic pressure is connected to the cosmological constant as a variable.

Abstract

We study the $P-V/r_{+}$ criticality and phase transition of quantum-corrected black hole in asymptotic safety (AS) gravity in the extended phase space. For the 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 the thermodynamic pressure. We find that for the quantum-corrected black hole there is a similar first-order phase transition to that of the van der Waals liquid/gas system. We also analyze the types of the phase transition at the critical points according to Ehrenfest's classification. It is shown that they are second-order phase transition.