Horizon Entropy from Quantum Gravity Condensates

Daniele Oriti, Daniele Pranzetti, and Lorenzo Sindoni
Phys. Rev. Lett. 116, 211301 – Published 24 May 2016

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.

  • Received 27 November 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.211301

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Daniele Oriti1,*, Daniele Pranzetti2,†, and Lorenzo Sindoni1,‡

  • 1Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany
  • 2Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy

  • *daniele.oriti@aei.mpg.de
  • dpranzetti@sissa.it
  • lorenzo.sindoni@aei.mpg.de

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Issue

Vol. 116, Iss. 21 — 27 May 2016

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