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

2001/04/30 by T. R. Govindarajan, T R Govindarajan, R. K. Kaul +3 · 4 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/18/15/303

published as Class.Quant.Grav.18:2877-2886,2001 · LaTeX, 10 pages, typos corrected, clarifications added

arxiv created 2001/05/09 · openalex publication_date 2001/07/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

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 four-dimensional canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the correct expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toroidal boundary of the black hole.

Citations

• Black hole in three-dimensional spacetime
• Thermodynamic ensembles and gravitation
• 2 + 1 dimensional gravity as an exactly soluble system
• Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions
• Geometry of the 2+1 Black Hole

Cited by

• Corrected entropy of BTZ black hole in tunneling approach
• Thermal fluctuations and black-hole entropy
• Asymptotic density of open p-brane states with zero-modes included
• Logarithmic correction to the Cardy-Verlinde formula in Achúcarro-Oritz black hole