Entropy in the classical and quantum polymer black hole models
Identifieur interne : 005544 ( Main/Curation ); 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
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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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<front><div type="abstract" xml:lang="en">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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<sourceDesc><biblStruct><analytic><title level="a">Entropy in the classical and quantum polymer black hole models</title>
<author><name sortKey="Livine, Etera R" sort="Livine, Etera R" uniqKey="Livine E" first="Etera R" last="Livine">Etera R. Livine</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Alle dItalie, Lyon 69007</wicri:regionArea>
<placeName><region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
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</affiliation>
<affiliation wicri:level="1"><country xml:lang="fr">Canada</country>
<wicri:regionArea>Perimeter Institute, 31 Caroline St N, Waterloo, ON N2L 2Y5</wicri:regionArea>
<wicri:noRegion>ON N2L 2Y5</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
</author>
<author><name sortKey="Terno, Daniel R" sort="Terno, Daniel R" uniqKey="Terno D" first="Daniel R" last="Terno">Daniel R. Terno</name>
<affiliation wicri:level="1"><country xml:lang="fr">Australie</country>
<wicri:regionArea>Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109</wicri:regionArea>
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<series><title level="j">Classical and Quantum Gravity</title>
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<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>2iqa</term>
<term>Area unit</term>
<term>Asymptotics</term>
<term>Bessel function</term>
<term>Black hole</term>
<term>Black hole entropy</term>
<term>Black hole horizon</term>
<term>Black hole horizons</term>
<term>Black holes</term>
<term>Class angle</term>
<term>Classical counterpart</term>
<term>Classical density</term>
<term>Classical model</term>
<term>Classical polyhedra</term>
<term>Classical polymer model</term>
<term>Closure</term>
<term>Closure constraint</term>
<term>Closure constraints</term>
<term>Coherent intertwiner states</term>
<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>
<term>Exterior geometry</term>
<term>External geometry</term>
<term>Fourier</term>
<term>Full closure constraints</term>
<term>Functionals</term>
<term>Fundamental representation</term>
<term>Fuzzy polyhedra</term>
<term>Gaussian</term>
<term>Gaussian approximation</term>
<term>Gaussian integrals</term>
<term>Geometric weight</term>
<term>Geometry state</term>
<term>Grav</term>
<term>Gravity</term>
<term>Group element</term>
<term>Hilbert</term>
<term>Hilbert space</term>
<term>Horizon area</term>
<term>Immirzi parameter</term>
<term>Interested reader</term>
<term>Intertwiner</term>
<term>Intertwiner space</term>
<term>Intertwiner states</term>
<term>Intertwiners</term>
<term>Irreducible representation</term>
<term>Large area</term>
<term>Linear regime</term>
<term>Livine</term>
<term>Loop gravity</term>
<term>Loop quantum gravity</term>
<term>Loop quantum gravity phys</term>
<term>Lowest pole</term>
<term>Matrix</term>
<term>Nmax</term>
<term>Normal vector</term>
<term>Normal vectors</term>
<term>Optimal number</term>
<term>Other hand</term>
<term>Perimeter institute</term>
<term>Phase space formulation</term>
<term>Phys</term>
<term>Polyhedron</term>
<term>Polymer</term>
<term>Polymer model</term>
<term>Present work</term>
<term>Previous work</term>
<term>Probability distribution</term>
<term>Puncture</term>
<term>Quantization</term>
<term>Quantized</term>
<term>Quantized polyhedra</term>
<term>Quantum</term>
<term>Quantum geometry</term>
<term>Quantum grav</term>
<term>Quantum level</term>
<term>Quantum model</term>
<term>Quantum polymer model</term>
<term>Regulator</term>
<term>Spinor</term>
<term>Spinor variables</term>
<term>Spinorial phase space</term>
<term>Spinors</term>
<term>Terno</term>
<term>Total area</term>
<term>Total boundary area</term>
<term>Unitary group</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en"><term>2iqa</term>
<term>Area unit</term>
<term>Asymptotics</term>
<term>Bessel function</term>
<term>Black hole</term>
<term>Black hole entropy</term>
<term>Black hole horizon</term>
<term>Black hole horizons</term>
<term>Black holes</term>
<term>Class angle</term>
<term>Classical counterpart</term>
<term>Classical density</term>
<term>Classical model</term>
<term>Classical polyhedra</term>
<term>Classical polymer model</term>
<term>Closure</term>
<term>Closure constraint</term>
<term>Closure constraints</term>
<term>Coherent intertwiner states</term>
<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>
<term>Exterior geometry</term>
<term>External geometry</term>
<term>Fourier</term>
<term>Full closure constraints</term>
<term>Functionals</term>
<term>Fundamental representation</term>
<term>Fuzzy polyhedra</term>
<term>Gaussian</term>
<term>Gaussian approximation</term>
<term>Gaussian integrals</term>
<term>Geometric weight</term>
<term>Geometry state</term>
<term>Grav</term>
<term>Gravity</term>
<term>Group element</term>
<term>Hilbert</term>
<term>Hilbert space</term>
<term>Horizon area</term>
<term>Immirzi parameter</term>
<term>Interested reader</term>
<term>Intertwiner</term>
<term>Intertwiner space</term>
<term>Intertwiner states</term>
<term>Intertwiners</term>
<term>Irreducible representation</term>
<term>Large area</term>
<term>Linear regime</term>
<term>Livine</term>
<term>Loop gravity</term>
<term>Loop quantum gravity</term>
<term>Loop quantum gravity phys</term>
<term>Lowest pole</term>
<term>Matrix</term>
<term>Nmax</term>
<term>Normal vector</term>
<term>Normal vectors</term>
<term>Optimal number</term>
<term>Other hand</term>
<term>Perimeter institute</term>
<term>Phase space formulation</term>
<term>Phys</term>
<term>Polyhedron</term>
<term>Polymer</term>
<term>Polymer model</term>
<term>Present work</term>
<term>Previous work</term>
<term>Probability distribution</term>
<term>Puncture</term>
<term>Quantization</term>
<term>Quantized</term>
<term>Quantized polyhedra</term>
<term>Quantum</term>
<term>Quantum geometry</term>
<term>Quantum grav</term>
<term>Quantum level</term>
<term>Quantum model</term>
<term>Quantum polymer model</term>
<term>Regulator</term>
<term>Spinor</term>
<term>Spinor variables</term>
<term>Spinorial phase space</term>
<term>Spinors</term>
<term>Terno</term>
<term>Total area</term>
<term>Total boundary area</term>
<term>Unitary group</term>
</keywords>
<keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Polymère</term>
</keywords>
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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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