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Journal Article

Fate of the Hoop Conjecture in Quantum Gravity


Chirco,  Goffredo
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Anzà, F., & Chirco, G. (2017). Fate of the Hoop Conjecture in Quantum Gravity. Physical Review Letters, 119: 231301. doi:10.1103/PhysRevLett.119.231301.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-0D88-D
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.