A note on cutting spin networks and the area spectrum in loop quantum gravity

TL;DR

This paper demonstrates that when a spin network is intersected by a surface in loop quantum gravity, the sum of crossing edge spins must be an integer, imposing a new restriction on the area spectrum relevant to black hole horizons.

Contribution

It introduces a novel restriction on the area spectrum in loop quantum gravity based on the crossing spins of spin networks at surfaces.

Findings

Sum of crossing edge spins must be an integer

Imposes constraints on black hole horizon area spectrum

Provides insight into quantum geometry in LQG

Abstract

In this paper, I show that if a spin network is cut by a surface separating space-time into two regions, the sum of spins of edges crossing the surface must be an integer. This gives a restriction on the area spectrum of such surfaces, including black hole horizons, in loop quantum gravity.