Black hole state counting in Loop Quantum Gravity: A number theoretical approach

Abstract

We give a practical method to exactly compute black hole entropy in the framework of Loop Quantum Gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and determine the number of solutions to the projection constraint analytically. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

Accepted for publication in Physical Review Letters

References in corpus (9)

• Quantum Geometry and Black Hole Entropy
• Black hole entropy in Loop Quantum Gravity
• Logarithmic correction to the Bekenstein-Hawking entropy
• Black hole entropy from Quantum Geometry
• An improved estimate of black hole entropy in the quantum geometry approach
• Black hole entropy quantization
• Quantum geometry and microscopic black hole entropy
• Black hole state degeneracy in Loop Quantum Gravity
• Number Partitioning on a Quantum Computer

Cited by in corpus (77)

• Black Holes in Loop Quantum Gravity
• Black hole entropy and SU(2) Chern-Simons theory
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Black hole entropy and isolated horizons thermodynamics
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
• Detailed black hole state counting in loop quantum gravity
• Potential gravitational-wave signatures of quantum gravity
• The SU(2) Black Hole entropy revisited
• Black Hole Entropy from complex Ashtekar variables
• The combinatorics of the SU(2) black hole entropy in loop quantum gravity
• $BF$ gravity
• Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
• Primordial power spectrum from the Dapor-Liegener model of loop quantum cosmology
• Black Holes as Quantum Gravity Condensates
• Geometric temperature and entropy of quantum isolated horizons
• Non-Gaussianity in Loop Quantum Cosmology
• Flux-area operator and black hole entropy
• Static isolated horizons: SU(2) invariant phase space, quantization, and black hole entropy
• On the computation of black hole entropy in loop quantum gravity
• Generating functions for black hole entropy in Loop Quantum Gravity
• Schwarzschild horizon dynamics and SU(2) Chern-Simons theory
• Breaking of isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes
• Surface terms, Asymptotics and Thermodynamics of the Holst Action
• A new look at Lorentz-Covariant Loop Quantum Gravity
• Generic isolated horizons in loop quantum gravity
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Fine-grained state counting for black holes in loop quantum gravity
• Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach
• Entropy of Isolated Horizons revisited
• Reformulation of the symmetries of first-order general relativity
• Testing the imposition of the Spin Foam Simplicity Constraints
• Loop Quantum Cosmology with Complex Ashtekar Variables
• Imprint of black hole area quantization and Hawking radiation on inspiraling binary
• A Lorentz-Covariant Connection for Canonical Gravity
• Statistical description of the black hole degeneracy spectrum
• Radiation from quantum weakly dynamical horizons in LQG
• Statistical and entanglement entropy for black holes in quantum geometry
• A topological limit of gravity admitting an SU(2) connection formulation
• Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy
• Entropy of black holes with arbitrary shapes in loop quantum gravity
• Spectra of geometric operators in three-dimensional LQG: From discrete to continuous
• Observations on interfacing loop quantum gravity with cosmology
• Quasi-normal modes and microscopic description of 2D black holes
• Entropy of Quantum Black Holes
• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Band structure in the polymer quantization of the harmonic oscillator
• Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
• The thermodynamic limit and black hole entropy in the area ensemble
• Gravastar under the framework of braneworld gravity II: effect of the Kuchowicz metric function
• Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
• Spectrum and Statistical Entropy of AdS Black Holes
• Gravity as an SU(1,1) gauge theory in four dimensions
• Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
• On the value of the Immirzi parameter and the horizon entropy
• The thermodynamics of isolated horizons in loop quantum gravity
• BTZ Black Hole Entropy and the Turaev-Viro model
• Quasi-normal modes and Microscopic Structure of the Schwarzschild Black Hole
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Quantum theory of charged isolated horizons
• On the distribution of the eigenvalues of the area operator in loop quantum gravity
• Revisiting the solution of the second-class constraints of the Holst action
• Barbero's formulation from a $BF$-type action with the Immirzi parameter
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Formation and Stability of Area Quantized Black Holes
• Towards a spin foam model description of black hole entropy
• Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations
• Entropy in Spin Foam Models: The Statistical Calculation
• Off-shell Noether currents and potentials for first-order general relativity
• Bose Condensation and the BTZ Black Hole
• Superradiant instability of area quantized Kerr black hole with discrete reflectivity
• The ADM papers and part of their modern legacy: loop quantum gravity
• Spontaneous particle creation by oscillating compact stars
• Signatures of an Emergent Gravity from Black Hole Entropy
• Black Hole Entropy in Loop Quantum Gravity and Number Theory
• A note on cutting spin networks and the area spectrum in loop quantum gravity
• A quantum number theory