Fate of the Hoop Conjecture in Quantum Gravity

Physical Review Letters
Fabio Anzà, Goffredo Chirco

Abstract

We consider a closed region R 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 ∂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 interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.

References

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Citations

Feb 7, 2020·The European Physical Journal. C, Particles and Fields·Andrea AddaziNicolás Yunes

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