Quantum Geometry and Black Hole Entropy

1997/10/01 by Abhay Ashtekar, A. Ashtekar, John C. Baez +5 · 25 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Black hole thermodynamics #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Extremal black hole #Immirzi parameter #Loop quantum gravity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevlett.80.904

published as Phys.Rev.Lett. 80 (1998) 904-907 · Revtex, 8 pages, 1 figure

arxiv created 1997/10/01 · openalex publication_date 1998/02/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A ``black hole sector'' of nonperturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large nonrotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the Bekenstein-Hawking formula S\phantom\rule0ex0ex=\phantom\rule0ex0exA/4\ensuremathℓ_P². With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charge, which are not necessarily near extremal.

Citations

• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Loop space representation of quantum general relativity
• Immirzi parameter in quantum general relativity
• New Variables for Classical and Quantum Gravity

Cited by

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• Quasilocal first law for black hole thermodynamics
• Spectroscopy of a canonically quantized horizon
• Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology
• Entanglement as a source of black hole entropy
• Where are the black-hole entropy degrees of freedom?
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Black hole entropy from horizon conformal field theory
• Logarithmic corrections to black hole entropy, from the Cardy formula
• Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Black Hole Thermodynamics from Euclidean Horizon Constraints
• Horizons, Constraints, and Black Hole Entropy
• Varying constants, black holes, and quantum gravity
• Dynamic black-hole entropy
• Black hole entropy and the modified uncertainty principle: A heuristic analysis
• Inflationary scalar spectrum in loop quantum cosmology
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Black hole quantum tunnelling and black hole entropy correction
• Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics
• Loop quantum gravity [wikipedia]