New Framework Brings Linearized Gravity Into Factorization Algebras

A new paper published in General Relativity and Gravitation sets out to connect gravitational theory with factorization algebras, a fast-developing mathematical framework for organizing the observables of quantum field theories. The work, authored by Filip Dul, appears as volume 58, article number 123, and was published on 21 October 2026.

The central contribution is a translation of the causal structure of Lorentzian manifolds into categorical language. In the globally hyperbolic case, the author identifies a convenient equivalence of coverages, providing structural groundwork for treating spacetime regions algebraically.

The paper then shows that both perturbative general relativity and perturbative conformal gravity can be formulated as Batalin-Vilkovisky classical field theories. Establishing these gravitational theories within the Batalin-Vilkovisky framework places them on footing compatible with the factorization algebra approach.

The main result concerns linearized general relativity. The author demonstrates that the observables of this theory define a factorization algebra with particularly nice properties on the category of Ricci flat globally hyperbolic manifolds. This restricts attention to spacetimes that are both globally hyperbolic and Ricci flat.

Beyond the core construction, the paper presents several conjectures that arise in specific cases. These conjectures are primarily motivated by the study of black hole entropy interpreted as a conserved Noether charge, linking the algebraic framework to one of the central open problems in gravitational physics. The paper opens with an epigraph from Herman Melville's Moby-Dick, and the abstract frames the work as a step toward bringing gravitational theories into the factorization algebra framework rather than a complete treatment.

Subject of Research: Factorization algebras for perturbative and linearized gravity on globally hyperbolic manifolds

Article Title: Factorization algebras for linearized gravity

Article References: Dul, F. (2026). Factorization algebras for linearized gravity. General Relativity and Gravitation, 58(10), Article 123. https://doi.org/10.1007/s10714-026-03622-2

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03622-2

Keywords: factorization algebras, linearized gravity, general relativity, conformal gravity, Batalin-Vilkovisky formalism, globally hyperbolic manifolds, Ricci flat spacetimes, Lorentzian causal structure, black hole entropy, Noether charge, mathematical physics, quantum field theory