Abstract
We consider a closed region 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 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.
- Received 28 June 2017
DOI:https://doi.org/10.1103/PhysRevLett.119.231301
© 2017 American Physical Society