Generalized entropy for general subregions in quantum gravity

Understand

We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit.

• When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor.
• To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer.
• In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy.