The quantum of area $\Delta A=8\pi l_P^2$ and a statistical interpretation of black hole entropy

Abstract

In contrast to alternative values, the quantum of area $\Delta A=8\pi l_P^2$ does not follow from the usual statistical interpretation of black hole entropy; on the contrary, a statistical interpretation follows from it. This interpretation is based on the two concepts: nonadditivity of black hole entropy and Landau quantization. Using nonadditivity a microcanonical distribution for a black hole is found and it is shown that the statistical weight of black hole should be proportional to its area. By analogy with conventional Landau quantization, it is shown that quantization of black hole is nothing but the Landau quantization. The Landau levels of black hole and their degeneracy are found. The degree of degeneracy is equal to the number of ways to distribute a patch of area $8\pi l_P^2$ over the horizon. Taking into account these results, it is argued that the black hole entropy should be of the form $S_{bh}=2\pi \cdot \Delta \Gamma$, where the number of microstates is $\Delta \Gamma =A/8\pi l_P^2$. The nature of the degrees of freedom responsible for black hole entropy is elucidated. The applications of the new interpretation are presented. The effect of noncommuting coordinates is discussed.

arXiv comment12 pages, revtex, no figures; v.3, revised and enlarged; Sec. III "Quantization of black hole as Landau quantization" added; references added; conclusions changed in some points

References in corpus (32)

• The World as a Hologram
• On the Origin of Gravity and the Laws of Newton
• The holographic principle
• The Thermodynamics of Black Holes
• Dimensional Reduction in Quantum Gravity
• Equipartition of energy in the horizon degrees of freedom and the emergence of gravity
• Nonadditive entropy: the concept and its use
• Stability and Critical Phenomena of Black Holes and Black Rings
• Some Speculations about Black Hole Entropy in String Theory
• "Peireles Substitution" and Chern-Simons Quantum Mechanics
• Quantum tunneling and black hole spectroscopy
• Quantum Black Holes as Atoms
• High-energy gravitational scattering and black hole resonances
• Quantization of the black hole area as quantization of the angular momentum component
• Information Recovery From Black Holes
• On the "Universal" Quantum Area Spectrum
• Thermodynamics with long-range interactions: from Ising models to black-holes
• Black Hole Thermodynamics and Statistical Mechanics
• The entropy of black holes: a primer
• Area scaling entropies for gravitating systems
• Observations on noncommuting coordinates and on fields depending on them
• Role of Horizons in Semiclassical Gravity: Entropy and the Area Spectrum
• Entropy of gravitating systems: scaling laws versus radial profiles
• Mass Spectrum for Black Holes in Generic 2-D Dilaton Gravity
• Black Hole Entropy and the Problem of Universality
• A note about the quantum of area in a non-commutative space
• Projection on higher Landau levels and non-commutative geometry
• Quantum Black Holes: the Event Horizon as a Fuzzy Sphere
• A brief commentary on black hole entropy
• Non-Boltzmann Statistics as an Alternative to Holography
• On the Observability of Quantum Information Radiated from a Black Hole
• Equilibrium temperature anisotropy and black-hole analogues

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• Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
• Black hole spectroscopy via adiabatic invariance
• Thermodynamics and Spectroscopy of Schwarzschild black hole surrounded by Quintessence
• On black hole spectroscopy via adiabatic invariance
• Quantization of rotating linear dilaton black holes
• A Note on the Lower Bound of Black Hole Area Change in Tunneling Formalism
• (1+1)-Dimensional Entropic Gravity
• Does Entropic Gravity Bound the Masses of the Photon and Graviton?
• Holographic Shell Model: Stack Data Structure inside Black Holes
• Gravitational surface Hamiltonian and entropy quantization
• Central charge
• Black Hole Motion in Entropic Reformulation of General Relativity
• Microcanonical distribution for black hole with allowance for nonadditivity
• The entropy and mean separation between energy levels of black hole