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

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

1997-10-22

arxiv.org/abs/gr-qc/9710106v2

Phys.Rev. D57 (1998) 4917-4924

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, Latex, one new reference added

Scientific paper

10.1103/PhysRevD.57.4917

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.

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