Quantum correction to the entropy of the (2+1)-dimensional black hole

The thermodynamics of the (2+1)-dimensional nonrotating black hole of Bañados, Teitelboim, and Zanelli is discussed. The first quantum correction to the Bekenstein-Hawking entropy is evaluated within the on-shell Euclidean formalism, making use of the related Chern-Simons representation of three-dimensional gravity. Horizon and ultraviolet divergences in the quantum correction are dealt with by a renormalization of the Newton constant. It is argued that the quantum correction due to the gravitational field shrinks the effective radius of a hole and becomes more and more important as the evaporation process goes on, while the area law is not violated.