General covariance and boundary symmetry algebras

Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, UMR 7332 - 13288 Marseille, France

Received: 18 February 2025
Accepted: 19 March 2025

Abstract

In general relativity as well as gauge theories, non-trivial symmetries can appear at boundaries. In the presence of radiation some of the symmetries are not Hamiltonian vector fields, hence the definition of charges for the symmetries becomes delicate. It can lead to the problem of field-dependent 2-cocycles in the charge algebra, as opposed to the central extensions allowed in standard classical mechanics. We show that if the Wald-Zoupas prescription is implemented, its covariance requirement guarantees that the algebra of Noether currents at the boundary is free of field-dependent 2-cocycles, and its stationarity requirement further removes central extensions. Therefore the charge algebra admits at most a time-independent field-dependent 2-cocycle, whose existence depends on the boundary conditions. We then report on new results for asymptotic symmetries at future null infinity that can be derived with this approach.