Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy

Abstract

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be $2^n$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U(2)\equiv U(1)\times SU(2)$ symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a {\it global} quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the $n$-th area eigenvalue is reduced to $2^n/n^{3/2}$ for large $n$, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of {\it two} building blocks.

15 pages, Revtex, to appear in Phys. Rev. D

References in corpus (27)

• The Thermodynamics of Black Holes
• Logarithmic correction to the Bekenstein-Hawking entropy
• Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
• General Logarithmic Corrections to Black Hole Entropy
• Conformal description of horizon's states
• Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• An Exact Black Hole Entropy Bound
• Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula
• Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach
• Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited
• Quantum Mechanics of Charged Black Holes
• Exact Results for the BTZ Black Hole
• A new holographic entropy bound from quantum geometry
• Entropy using Path Integrals for Quantum Black Hole Models
• Building blocks of a black hole
• Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole
• Hamiltonian Thermodynamics of Charged Black Holes
• Schwarzschild black hole as a grand canonical ensemble
• Gravitational Statistical Mechanics: A model
• Black hole area quantization
• Quantum Aspects of Black Hole Entropy
• Quantum Mechanics of a Black Hole
• Why is the black hole entropy (almost) linear in the horizon area?
• Schwarzschild Black Hole Quantum Statistics from Z(2) Orientation Degrees of Freedom and its Relations to Ising Droplet Nucleation
• On the Universality of the Entropy-Area Relation
• How to interpret black hole entropy?

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