Quantum Corrections to the Thermodynamics of Charged 2-D Black Holes

TL;DR

This paper computes one-loop quantum corrections to the thermodynamics of 2D charged black holes, considering matter fields and back reaction effects, and applies the results to specific black hole models.

Contribution

It introduces a formalism for calculating quantum corrections to black hole thermodynamics in generic 2D dilaton gravity, including charged and rotating black holes.

Findings

Quantum corrections modify black hole entropy and energy.

Back reaction effects are significant in thermodynamic calculations.

Results are applied to charged and BTZ black holes.

Abstract

We consider one-loop quantum corrections to the thermodynamics of a black hole in generic 2-dimensional dilaton gravity. The classical action is the most general diffeomorphism invariant action in 1+1 space-time dimensions that contains a metric, dilaton, and Abelian gauge field, and having at most second derivatives of the fields. Quantum corrections are introduced by considering the effect of matter fields conformally coupled to the metric and non-minimally coupled to the dilaton. Back reaction of the matter fields (via non-vanishing trace conformal anomaly) leads to quantum corrections to the black hole geometry. Quantum corrections also lead to modifications in the gravitational action and hence in expressions for thermodynamic quantities. One-loop corrections to both geometry and thermodynamics (energy, entropy) are calculated for the generic dilaton theory. This formalism is applied to a charged black hole in spherically symmetric gravity and to a rotating BTZ black hole.