On the fate of the Hoop Conjecture in quantum gravity

Abstract

We consider a closed region $R$ of 3d quantum space modeled by $SU(2)$ spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary $\partial R$ 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 interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity.

7 pages, 2 figures, minor improvements

References in corpus (4)

• Typicality for Generalized Microcanonical Ensembles
• Polyhedra in loop quantum gravity
• Bulk Entropy in Loop Quantum Gravity
• Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks

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• On the Kalb-Ramond modified Lorentz violating hairy black holes and Thorne's hoop conjecture
• Curvature from multipartite entanglement in quantum gravity states
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners
• Investigations on hoop conjecture for horizonless spherical charged stars
• Testing generalized spacetimes for black holes using the Hod function representation of the hoop conjecture