Factorization Algebras for Linearized Gravity

Abstract

The purpose of this work is to bring gravitational theories into play within the quickly developing framework of factorization algebras. We fit the causal structure of Lorentzian manifolds into categorical language, and in the globally hyperbolic case discover a convenient equivalence of coverages. Then, we show how both perturbative general relativity and perturbative conformal gravity define Batalin-Vilkovisky classical field theories. Finally, we describe how the observables of linearized general relativity define a particularly nice factorization algebra on the category of all globally hyperbolic manifolds and present a few conjectures which arise in specific cases, primarily motivated by the study of black hole entropy as a conserved Noether charge.