Entropy in the classical and quantum polymer black hole models
Identifieur interne : 005544 ( Main/Exploration ); précédent : 005543; suivant : 005545Entropy in the classical and quantum polymer black hole models
Auteurs : Etera R. Livine [France, Canada] ; Daniel R. Terno [Australie]Source :
- Classical and Quantum Gravity [ 0264-9381 ] ; 2012-11-21.
Descripteurs français
- Pascal (Inist)
- Wicri :
- topic : Cosmologie, Polymère.
English descriptors
- KwdEn :
- 2iqa, Area unit, Asymptotics, Bessel function, Black hole, Black hole entropy, Black hole horizon, Black hole horizons, Black holes, Class angle, Classical counterpart, Classical density, Classical model, Classical polyhedra, Classical polymer model, Closure, Closure constraint, Closure constraints, Coherent intertwiner states, Coherent intertwiners, Coherent states, Constraint, Corrections, Correlations, Cosmology, D3vi, Dynamics, Entropy, Equidistant spectrum, Equivalently, Essential role, Exact intertwiner, Exterior geometry, External geometry, Fourier, Full closure constraints, Functionals, Fundamental representation, Fuzzy polyhedra, Gaussian, Gaussian approximation, Gaussian integrals, Geometric weight, Geometry state, Grav, Gravity, Group element, Hilbert, Hilbert space, Horizon area, Immirzi parameter, Interested reader, Intertwiner, Intertwiner space, Intertwiner states, Intertwiners, Irreducible representation, Large area, Linear regime, Livine, Loop gravity, Loop quantum gravity, Loop quantum gravity phys, Lowest pole, Matrix, Models, Nmax, Normal vector, Normal vectors, Optimal number, Other hand, Perimeter institute, Phase space formulation, Phys, Polyhedron, Polymer, Polymer model, Polymers, Present work, Previous work, Probability distribution, Puncture, Quantization, Quantized, Quantized polyhedra, Quantum, Quantum geometry, Quantum grav, Quantum level, Quantum model, Quantum polymer model, Regulator, SU(2) theory, Spinor, Spinor variables, Spinorial phase space, Spinors, Terno, Three dimensional space, Total area, Total boundary area, Unitary group.
- Teeft :
- 2iqa, Area unit, Asymptotics, Bessel function, Black hole, Black hole entropy, Black hole horizon, Black hole horizons, Black holes, Class angle, Classical counterpart, Classical density, Classical model, Classical polyhedra, Classical polymer model, Closure, Closure constraint, Closure constraints, Coherent intertwiner states, Coherent intertwiners, Coherent states, Constraint, D3vi, Entropy, Equidistant spectrum, Equivalently, Essential role, Exact intertwiner, Exterior geometry, External geometry, Fourier, Full closure constraints, Functionals, Fundamental representation, Fuzzy polyhedra, Gaussian, Gaussian approximation, Gaussian integrals, Geometric weight, Geometry state, Grav, Gravity, Group element, Hilbert, Hilbert space, Horizon area, Immirzi parameter, Interested reader, Intertwiner, Intertwiner space, Intertwiner states, Intertwiners, Irreducible representation, Large area, Linear regime, Livine, Loop gravity, Loop quantum gravity, Loop quantum gravity phys, Lowest pole, Matrix, Nmax, Normal vector, Normal vectors, Optimal number, Other hand, Perimeter institute, Phase space formulation, Phys, Polyhedron, Polymer, Polymer model, Present work, Previous work, Probability distribution, Puncture, Quantization, Quantized, Quantized polyhedra, Quantum, Quantum geometry, Quantum grav, Quantum level, Quantum model, Quantum polymer model, Regulator, Spinor, Spinor variables, Spinorial phase space, Spinors, Terno, Total area, Total boundary area, Unitary group.
Abstract
We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of almost-closed polyhedra.
Url:
DOI: 10.1088/0264-9381/29/22/224012
Affiliations:
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<term>Black hole entropy</term>
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<term>Classical density</term>
<term>Classical model</term>
<term>Classical polyhedra</term>
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<term>Closure constraint</term>
<term>Closure constraints</term>
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<term>Coherent intertwiners</term>
<term>Coherent states</term>
<term>Constraint</term>
<term>Corrections</term>
<term>Correlations</term>
<term>Cosmology</term>
<term>D3vi</term>
<term>Dynamics</term>
<term>Entropy</term>
<term>Equidistant spectrum</term>
<term>Equivalently</term>
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<term>Fourier</term>
<term>Full closure constraints</term>
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<term>Fundamental representation</term>
<term>Fuzzy polyhedra</term>
<term>Gaussian</term>
<term>Gaussian approximation</term>
<term>Gaussian integrals</term>
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<term>Geometry state</term>
<term>Grav</term>
<term>Gravity</term>
<term>Group element</term>
<term>Hilbert</term>
<term>Hilbert space</term>
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<term>Linear regime</term>
<term>Livine</term>
<term>Loop gravity</term>
<term>Loop quantum gravity</term>
<term>Loop quantum gravity phys</term>
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<term>Matrix</term>
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<term>Nmax</term>
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<term>Normal vectors</term>
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<term>Other hand</term>
<term>Perimeter institute</term>
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<term>Phys</term>
<term>Polyhedron</term>
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<term>Polymer model</term>
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<term>Previous work</term>
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<term>Three dimensional space</term>
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<term>Entropie</term>
<term>Espace 3 dimensions</term>
<term>Gravitation quantique à boucles</term>
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<term>Polyèdre</term>
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<term>Trou noir</term>
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<term>Classical model</term>
<term>Classical polyhedra</term>
<term>Classical polymer model</term>
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<term>Closure constraints</term>
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<term>Coherent intertwiners</term>
<term>Coherent states</term>
<term>Constraint</term>
<term>D3vi</term>
<term>Entropy</term>
<term>Equidistant spectrum</term>
<term>Equivalently</term>
<term>Essential role</term>
<term>Exact intertwiner</term>
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<term>Gravity</term>
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<term>Horizon area</term>
<term>Immirzi parameter</term>
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<front><div type="abstract">We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of almost-closed polyhedra.</div>
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