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キーワード:
General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Quantum Physics, quant-ph
要旨:
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.
