Quantum geometry and microscopic black hole entropy

Abstract

Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area $A_0$ are counted and the statistical entropy, as a function of the area, is obtained for $A_0$ up to $550l_{\mathrm{Pl}}^2$. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to $\gamma =0.274$, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.

10 pages, Revtex4 file, 7 new figures. Discussion expanded, same conclusions

References in corpus (10)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Quantum Geometry and Black Hole Entropy
• Black hole entropy in Loop Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• Quasinormal Modes, the Area Spectrum, and Black Hole Entropy
• Black hole entropy from Quantum Geometry
• The Immirzi parameter in quantum general relativity
• An improved estimate of black hole entropy in the quantum geometry approach
• Yang-Mills analogues of the Immirzi ambiguity
• How Is the Maximum Entropy of a Quantized Surface Related to Its Area?

Cited by in corpus (46)

• Black Holes in Loop Quantum Gravity
• Black hole state counting in Loop Quantum Gravity: A number theoretical approach
• Detailed black hole state counting in loop quantum gravity
• Black hole entropy quantization
• The combinatorics of the SU(2) black hole entropy in loop quantum gravity
• Renormalization and black hole entropy in Loop Quantum Gravity
• Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
• Quantum Gravity: A Brief History of Ideas and Some Prospects
• Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity
• Black Holes as Quantum Gravity Condensates
• Flux-area operator and black hole entropy
• Loop Quantum Gravity
• On the computation of black hole entropy in loop quantum gravity
• Generating functions for black hole entropy in Loop Quantum Gravity
• Probing Loop Quantum Gravity with Evaporating Black Holes
• Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity
• Fine-grained state counting for black holes in loop quantum gravity
• Black hole state degeneracy in Loop Quantum Gravity
• Polymeric Quantization and Black Hole Thermodynamics
• Non-commutative black holes of various genera in the connection formalism
• Statistical description of the black hole degeneracy spectrum
• Toward explaining black hole entropy quantization in loop quantum gravity
• Observations on interfacing loop quantum gravity with cosmology
• Emergence of symmetries
• Spectrum and Statistical Entropy of AdS Black Holes
• Black hole radiation spectrum in LQG: Isolated Horizon framework
• On the value of the Immirzi parameter and the horizon entropy
• Absence of log correction in entropy of large black holes
• Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
• Elementary charge and neutrino's mass from Planck length
• Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy Corrections
• Loop Quantum Corrected Einstein Yang-Mills Black Holes
• A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
• Canonical Partition function of Loop Black Holes
• Considering boundary conditions for black hole entropy in loop quantum gravity
• Two-oscillator Kantowski-Sachs model of the Schwarzschild black hole interior
• On the black hole singularity issue in loop quantum gravity
• Towards a spin foam model description of black hole entropy
• Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Schwarzschild Black Hole
• Statistical analysis of entropy correction from topological defects in Loop Black Holes
• Entropy in Spin Foam Models: The Statistical Calculation
• Spectrum of area in the Faddeev formulation of gravity
• Approximation of the naive black hole degeneracy
• Black Hole Entropy in Loop Quantum Gravity and Number Theory
• Black hole entropy with and without log correction in loop quantum gravity
• Quantum and classical areas of black hole thermodynamics