We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one. © 2016 American Physical Society.

Horizon entropy from quantum gravity condensates / Oriti, D.; Pranzetti, Daniele; Sindoni, L.. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 116:21(2016), pp. 1-6. [10.1103/PhysRevLett.116.211301]

Horizon entropy from quantum gravity condensates

Pranzetti, Daniele;
2016-01-01

Abstract

We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one. © 2016 American Physical Society.
2016
116
21
1
6
219902
https://arxiv.org/abs/1510.06991
http://inspirehep.net/record/1400585
http://cdsads.u-strasbg.fr/abs/2016PhRvL.116u1301O
Oriti, D.; Pranzetti, Daniele; Sindoni, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32576
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