Center-less BMS charge algebra

TL;DR

This paper demonstrates that implementing the Wald-Zoupas prescription results in a center-less BMS charge algebra at null infinity, emphasizing the importance of covariance in defining gravitational charges and resolving ambiguities.

Contribution

It refines the covariance prescription for BMS charges, introduces a new aspect for Geroch's super-momentum, and shows the algebra is center-less without 2-cocycles when covariance is properly implemented.

Findings

Charges realize the BMS algebra without central extension.

A Wald-Zoupas symplectic potential exists for extended BMS with singular vectors.

The algebra of Noether currents is center-less at any cut of null infinity.

Abstract

We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects.