Logarithmic corrections to black hole entropy, from the Cardy formula

2000/05/31 by S. Carlip · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Logarithm #Mathematical analysis #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum electrodynamics #Quantum mechanics #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/17/20/302

published as Class.Quant.Grav.17:4175-4186,2000 · 14 pages, LaTeX; v2: appendix added on relation of Cardy formula to string theory ``level density''; v3: appendix added on quantum corrections to central charge; minor corrections and added references; to appear in Class. Quant. Grav

arxiv created 2000/08/22 · openalex publication_date 2000/09/19 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Many recent attempts to calculate black hole entropy from first principles rely on conformal field theory techniques. By examining the logarithmic corrections to the Cardy formula, I compute the first-order quantum correction to the Bekenstein-Hawking entropy in several models, including those based on asymptotic symmetries, horizon symmetries and certain string theories. Despite very different physical assumptions, these models all give a correction proportional to the logarithm of the horizon size, and agree qualitatively with recent results from `quantum geometry' in 3 + 1 dimensions. There are some indications that even the coefficient of the correction may be universal, up to differences that depend on the treatment of angular momentum and conserved charges.

Citations

• Quantum States of Black Holes
• Entropy of the Schwarzschild black hole and the string–black-hole correspondence
• Black hole in three-dimensional spacetime
• Statistical mechanics of the (2+1)-dimensional black hole
• Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes
• Black hole explosions?
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• Quantum Geometry and Black Hole Entropy
• Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions
• Microscopic Origin of the Bekenstein-Hawking Entropy

Cited by

• Distinguishing Black Hole Microstates using Holevo Information
• Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole
• Log corrections to entropy of three dimensional black holes with soft hair
• Black hole entropy from the boundary conformal structure in 3D gravity with torsion
• Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle
• Quantum gravity partition functions in three dimensions