Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

Details Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

2001-04-03

arxiv.org/abs/gr-qc/0104010v3

Class.Quant.Grav.18:2877-2886,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 10 pages, typos corrected, clarifications added

Scientific paper

10.1088/0264-9381/18/15/303

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.

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