Centerless BMS charge algebra

Abstract

We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the Bondi-Van der Burg–Metzner-Sachs (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 supermomentum 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 centerless. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and nonradiative. More precisely, superrotation fluxes act covariantly, but superrotation 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. Published by the American Physical Society 2024