# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Fate of the Hoop Conjecture in Quantum Gravity

##### MPS-Authors

##### External Ressource

No external resources are shared

##### Fulltext (public)

1703.05241.pdf

(Preprint), 527KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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

##### 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.