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

Abstract

The thermodynamic properties of the (2+1)-dimensional non-rotating black hole of Bañados, 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.

14 pages, Latex, one new reference added

References in corpus (2)

• Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant
• Quantum correction to thermodynamical entropy of black hole

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• A Selberg zeta function for warped AdS${}_3$ black holes
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