On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes

TL;DR

This paper investigates quantum corrections to the thermodynamics of charged black holes in a 2D model, revealing modifications to entropy and energy due to quantum effects and backreaction, using an off-shell approach with conical singularities.

Contribution

It introduces a consistent off-shell framework for quantum-corrected black hole thermodynamics, including the effects of conical defects and backreaction in a 2D reduction of Einstein-Maxwell theory.

Findings

Quantum corrections modify the entropy-horizon area relation.

Backreaction effects are computed perturbatively.

The hot gas contribution to thermodynamics can be isolated or eliminated.

Abstract

Quantum corrections are studied for a charged black hole in a two-dimensional model obtained by spherisymmetric reduction of the 4D Einstein-Maxwell theory. The classical (tree-level) thermodynamics is re-formulated in the framework of the off-shell approach, considering systems at arbitrary temperature. This implies a conical singularity at the horizon and modifies the gravitational action by terms defined on the horizon. A consistent variational procedure for the action functional is formulated. It is shown that the free energy reaches an extremum on the regular manifold with $T=T_H$. The one-loop contribution to the action in the Liouville-Polyakov form is re-examined. All the boundary terms are taken into account and the dependence on the state of the quantum field is established. The modification of the Liouville-Polyakov term for a 2D space with a conical defect is derived. The backreaction of the Hawking radiation on the geometry is studied and the quantum-corrected black hole metric is calculated perturbatively. Within the off-shell approach the one-loop thermodynamical quantities, energy and entropy, are found. They are shown to contain a part due to hot gas surrounding he black hole and a part due to the hole itself. It is noted that the contribution of the hot gas can be eliminated by appropriate choice of the (generally, non-flat) reference geometry. The deviation of the {\it `` entropy - horizon area''} relation for the quantum-corrected black hole from the classical law is discovered and possible physical consequences are discussed.