Ergodic Concepts for a Self-Organizing Trivalent Spin Network: A Path to $(2+1)$-dimensional Black Hole Entropy

Abstract

We consider, from a dynamical systems point of view, a trivalent spin network model in Loop Quantum Gravity presenting self-organized criticality (SOC), arising from a spin propagation dynamics. We obtain a partition function for the domains of stability connecting gauge non-invariant avalanches, leading to an entropy formula for the asymptotic SOC state. The microscopic origin of this SOC entropy is therefore given by the excitation-relaxation spin dynamics in the avalanche cycle. The puncturing of TSN edges participating in the avalanche are counted in terms of an ensemble perimeter over the implicit avalanches. By identifying this perimeter with that of an isolated $(2+1)$-dim. black hole horizon, we conjecture that the SOC entropy reduces to the Bekenstein-Hawking perimeter-entropy law for the Bañados, Teitelboim, and Zanelli (BTZ) black hole, by an appropriate adjustment of a potential function based on the thermodynamical formalism of Sinai, Ruelle and Bowen.

arXiv comment15 pages, 2 figures. Final version, accepted for publication in Annalen der Physik

References in corpus (39)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Black Hole Entropy from Near-Horizon Microstates
• Black hole entropy in Loop Quantum Gravity
• The Spin Foam Approach to Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• The (2+1)-Dimensional Black Hole
• Hawking Radiation and Black Hole Thermodynamics
• Quantum Gravity: a Progress Report
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Quantum gravity, shadow states, and quantum mechanics
• Power laws and Self-Organized Criticality in Theory and Nature
• Black hole boundaries
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• What We Don't Know about BTZ Black Hole Entropy
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Black Holes in Loop Quantum Gravity
• Counting surface states in the loop quantum gravity
• Corrected form of the first law of thermodynamics for regular black holes
• Entropy of Three-Dimensional Black Holes in String Theory
• Regular black holes in three dimensions
• Quantum Gravity Evolution in the Hawking Radiation of a Rotating Regular Hayward Black Hole
• A new bound on polymer quantization via an opto-mechanical setup
• Aging in a Model of Self-Organized Criticality
• Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity
• Thermal Fluctuations Evolution of the New Schwarzschild Black Hole
• Ising Spin Network States for Loop Quantum Gravity: a Toy Model for Phase Transitions
• Self-Organized Criticality and Thermodynamic formalism
• Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality
• Horizons, Constraints, and Black Hole Entropy
• Asymptotes of Space Curves
• Propagating spin modes in canonical quantum gravity
• Self-Organized Criticality in a Transient System
• Self-organized criticality in quantum gravity
• The Barbero-Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity
• Canonical Partition function of Loop Black Holes
• Self-organized critical behavior: the evolution of frozen spin networks model in quantum gravity
• Expanding and Self-Organizing 2D Universe Models Emerging from Frozen Trivalent Spin Networks