Fate of the Hoop Conjecture in Quantum Gravity

Fabio Anzà and Goffredo Chirco
Phys. Rev. Lett. 119, 231301 – Published 4 December 2017
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Abstract

We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne’s “hoop conjecture,” at the core of the formation of a horizon in general relativity.

  • Figure
  • Received 28 June 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.231301

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsQuantum Information, Science & Technology

Authors & Affiliations

Fabio Anzà1,2 and Goffredo Chirco3

  • 1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 2The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 Trieste, Italy
  • 3Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476 Potsdam, Germany

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Issue

Vol. 119, Iss. 23 — 8 December 2017

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