Quantum-corrected black hole thermodynamics from the gravitational path integral

TL;DR

This paper investigates quantum corrections to black hole thermodynamics using the Euclidean path integral, revealing modified phase structures and the emergence of zero-order phase transitions due to off-shell effects.

Contribution

It introduces a method to include off-shell geometries in the path integral, deriving quantum-corrected thermodynamics and phase diagrams for Reissner-Nordstrom-AdS black holes.

Findings

Modified phase diagram with richer phase structure

Shrinkage of first-order transition region

Emergence of zero-order phase transitions

Abstract

Exploring quantum effects from black hole thermodynamics has always been a pivotal topic. In recent years, the free energy landscape and ensemble-averaged theory based on the Euclidean path integral approach have provided further understanding of the statistical aspects of the black hole system. We investigate the quantum-corrected thermodynamics of the Reissner-Nordstrom-AdS black hole by including off-shell geometries in the path integral. We obtain a one-loop effective action by considering the subleading-order terms in the ensemble-averaged theory, and verify that the effective thermodynamic quantities consistent with the effective action define a valid thermodynamics. Furthermore, the phase diagram was modified by the off-shell effects, resulting in a more abundant phase structure. We discover that the traditional black hole thermodynamics can be recovered in the semi-classical limit. The region of first-order phase transitions shrinks and zero-order phase transitions emerge when off-shell effects are included. The results provide new perspectives for understanding the quantum corrections in black hole thermodynamics.