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arXiv · 1703.05241

On the fate of the Hoop Conjecture in quantum gravity

Fabio Anzà·Goffredo Chirco
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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.

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Fabio Anzà, Goffredo Chirco. 2017-03-21. On the fate of the Hoop Conjecture in quantum gravity. https://doi.org/10.1103/physrevlett.119.231301

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