Abstract

I will describe a derivation of the generalized second law of black hole horizons from the perspective of gravitational von Neumann algebras. The algebra is constructed via a crossed product construction, and consists of quantum field operators dressed to the asymptotic ADM mass. Using properties of half-sided modular inclusions for the black hole horizon, I will argue that this algebra is a type II von Neumann algebra, and hence possesses a well-defined trace and renormalized entropy. By consistently normalizing the trace between cuts, the entropy of semiclassical states can be shown to increase toward the future. I will also discuss interesting features of working with interacting quantum fields and asymptotically flat black holes, and relate these to algebraic features of the half-sided modular inclusion; namely, the concept of a singular inclusion and an algebra at infinity.