Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole

TL;DR

This paper calculates the first quantum correction to the entropy of a (2+1)-dimensional black hole using Euclidean formalism and Chern-Simons theory, showing the correction's significance during evaporation.

Contribution

It provides a novel evaluation of quantum entropy correction for the (2+1)-D black hole within the Chern-Simons framework, maintaining the area law.

Findings

Quantum correction shrinks the black hole's effective radius.

Correction becomes more significant during evaporation.

Area law remains valid despite quantum effects.

Abstract

The thermodynamic properties of the (2+1)-dimensional non-rotating black hole of Ba\~nados, Teitelboim and Zanelli are 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 the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum correction are dealt with 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 soon as the evaporation process goes on, while the area law is not violated.