Thermal Fluctuations and Black Hole Entropy

Abstract

In this paper, we consider the effect of thermal fluctuations on the entropy of both neutral and charged black holes. We emphasize the distinction between fixed and fluctuating charge systems; using a canonical ensemble to describe the former and a grand canonical ensemble to study the latter. Our novel approach is based on the philosophy that the black hole quantum spectrum is an essential component in any such calculation. For definiteness, we employ a uniformly spaced area spectrum, which has been advocated by Bekenstein and others in the literature. The generic results are applied to some specific models; in particular, various limiting cases of an (arbitrary-dimensional) AdS-Reissner-Nordstrom black hole. We find that the leading-order quantum correction to the entropy can consistently be expressed as the logarithm of the classical quantity. For a small AdS curvature parameter and zero net charge, it is shown that, independent of the dimension, the logarithmic prefactor is +1/2 when the charge is fixed but +1 when the charge is fluctuating.We also demonstrate that, in the grand canonical framework, the fluctuations in the charge are large, $\Delta Q\sim \Delta A\sim S_{BH}^{1/2}$, even when $<Q>=0$. A further implication of this framework is that an asymptotically flat, non-extremal black hole can never achieve a state of thermal equilibrium.

arXiv comment25 pages, Revtex; references added and corrected, and some minor changes

References in corpus (46)

• Large N Field Theories, String Theory and Gravity
• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Charged AdS Black Holes and Catastrophic Holography
• Quantum Geometry and Black Hole Entropy
• 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
• Spectroscopy of the quantum black hole
• The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
• Universality of Quantum Entropy for Extreme Black Holes
• Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
• Area spectrum of the Schwarzschild black hole
• On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To Quantum Corrections
• Entropy of Schwarzschild black hole and string-black hole correspondence
• Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics
• 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
• Logarithmic Corrections to Black Hole Entropy and AdS/CFT Correspondence
• Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited
• A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
• Quantum Mechanics of Charged Black Holes
• On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes
• Canonical Quantum Statistics of an Isolated Schwarzschild Black Hole with a Spectrum E_n = sigma sqrt{n} E_P
• Exact Results for the BTZ Black Hole
• A new holographic entropy bound from quantum geometry
• Quantum Corrections to the Thermodynamics of Charged 2-D Black Holes
• One-Loop Corrected Thermodynamics of the Extremal and Non-Extremal Spinning BTZ Black Hole
• Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
• Discrete Spectra of Charged Black Holes
• Quantum-mechanical model of the Kerr-Newman black hole
• Quantum Spectrum for a Kerr-Newman Black Hole
• Entropy using Path Integrals for Quantum Black Hole Models
• Building blocks of a black hole
• Kerr Black Hole as a Quantum Rotator
• Schwarzschild black hole as a grand canonical ensemble
• Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity
• Gravitational Statistical Mechanics: A model
• Black hole area quantization
• Quantum Aspects of Black Hole Entropy
• Quantum gravitational corrections to black hole geometries
• The Energy Spectrum of the Membrane effective Model for Quantum Black Holes
• On the Universality of the Entropy-Area Relation
• Quantum-Corrected Entropy for 1+1-Dimensional Gravity Revisited

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• On Hawking Radiation as Tunneling with Logarithmic Corrections
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• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
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• Canonical entropy of three-dimensional BTZ black hole
• On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation
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• On Black Hole Entropy Corrections in the Grand Canonical Ensemble
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
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