Quantum corrections to the thermodynamics of charged 2D black holes

Abstract

We consider one-loop quantum corrections to the thermodynamics of a black hole in generic two-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 nonminimally coupled to the dilaton. Back reaction of the matter fields (via nonvanishing 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 theory. The formalism is then applied to a charged black hole in spherically symmetric gravity and to a rotating Bañados-Teitelboim-Zanelli black hole.