Quantum Black Holes: Entropy and Entanglement on the Horizon
arXiv:gr-qc/0508085 · doi:10.1016/j.nuclphysb.2006.02.012
Abstract
We are interested in black holes in Loop Quantum Gravity (LQG). We study the simple model of static black holes: the horizon is made of a given number of identical elementary surfaces and these small surfaces all behaves as a spin-s system accordingly to LQG. The chosen spin-s defines the area unit or area resolution, which the observer uses to probe the space(time) geometry. For s=1/2, we are actually dealing with the qubit model, where the horizon is made of a certain number of qubits. In this context, we compute the black hole entropy and show that the factor in front of the logarithmic correction to the entropy formula is independent of the unit s. We also compute the entanglement between parts of the horizon. We show that these correlations between parts of the horizon are directly responsible for the asymptotic logarithmic corrections. This leads us to speculate on a relation between the evaporation process and the entanglement between a pair of qubits and the rest of the horizon. Finally, we introduce a concept of renormalisation of areas in LQG.
Revtex4, 25 pages, 4 figures
References in corpus (10)
- On the quantum, classical and total amount of correlations in a quantum state
- Hawking Radiation and Black Hole Thermodynamics
- Measures and dynamics of entangled states
- Classical and quantum communication without a shared reference frame
- Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
- Relativistically invariant quantum information
- Decoherence-full subsystems and the cryptographic power of a private shared reference frame
- Symmetry and entropy of black hole horizons
- Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
- Entanglement of zero angular momentum mixtures and black hole entropy
Cited by in corpus (71)
- Reference frames, superselection rules, and quantum information
- Entanglement entropy of black holes
- Black Hole Thermodynamics
- Black hole entropy and SU(2) Chern-Simons theory
- Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
- The Fine Structure of SU(2) Intertwiners from U(N) Representations
- The SU(2) Black Hole entropy revisited
- Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
- Black Hole Entropy from complex Ashtekar variables
- Renormalization and black hole entropy in Loop Quantum Gravity
- Dynamics for a 2-vertex Quantum Gravity Model
- Generalized quantum gravity condensates for homogeneous geometries and cosmology
- Symmetries, Horizons, and Black Hole Entropy
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
- Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
- Boundary unitarity and the black hole information paradox
- Black Holes as Quantum Gravity Condensates
- Black Hole Thermodynamics and Statistical Mechanics
- Static isolated horizons: SU(2) invariant phase space, quantization, and black hole entropy
- Relativistic quantum information and time machines
- Bulk Entropy in Loop Quantum Gravity
- Thermodynamics, phase transitions and Ruppeiner geometry for Einstein-dilaton Lifshitz black holes in the presence of Maxwell and Born-Infeld electrodynamics
- Black hole horizons from within loop quantum gravity
- Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
- Symmetry and entropy of black hole horizons
- Generic isolated horizons in loop quantum gravity
- New Hamiltonians for loop quantum cosmology with arbitrary spin representations
- Effective Conformal Descriptions of Black Hole Entropy: A Review
- Black holes in full quantum gravity
- Black Hole Thermodynamics from Euclidean Horizon Constraints
- Fisher Metric, Geometric Entanglement and Spin Networks
- Generic degeneracy and entropy in loop quantum gravity
- Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
- A topological limit of gravity admitting an SU(2) connection formulation
- Matrix Models as Non-commutative Field Theories on R^3
- Typicality in spin network states of quantum geometry
- Black Hole Entropy and the Problem of Universality
- Dynamical evaporation of quantum horizons
- Entropy of Quantum Black Holes
- From Planck area to graph theory: Topologically distinct black hole microstates
- Spectroscopy of a canonically quantized horizon
- Symmetry enforced entanglement in maximally mixed states
- Quantum simulations of a qubit of space
- On the fate of the Hoop Conjecture in quantum gravity
- Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
- Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
- Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
- Hidden Messenger from Quantum Geometry: Towards Information Conservation in Quantum Gravity
- Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction
- Entropy in the Classical and Quantum Polymer Black Hole Models
- Black Hole Entropy and the Problem of Universality
- Loop Quantum Gravity's Boundary Maps
- Holographic Shell Model: Stack Data Structure inside Black Holes
- Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
- Holographic entanglement in spin network states: a focused review
- The entropic boundary law in BF theory
- Loop Quantum Gravity and Quantum Information
- Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
- Quantum corrections to the Hawking radiation spectrum
- Considering boundary conditions for black hole entropy in loop quantum gravity
- Intertwiner Entanglement Excitation and Holonomy Operator
- The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
- Spherically-symmetric geometries in a matter reference frame as quantum gravity condensates
- Entropy in Spin Foam Models: The Statistical Calculation
- Self-Relative (or Machian) Information: Entropy-Area Relation
- Aspects of quantum gravity
- Horizon thermodynamics in theory
- Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity
- The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
- Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
- Approximation of the naive black hole degeneracy