“Conserved charges” of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory *

Abstract

Abstract The asymptotic symmetries in the Brans-Dicke theory are analyzed using Penrose's conformal completion method, which is independent of the coordinate system used. These symmetries, indeed, include supertranslations and Lorentz transformations for an asymptotically flat spacetime. With the Wald-Zoupas formalism, “conserved charges” and fluxes of the Bondi-Metzner-Sachs algebra are computed. The scalar degree of freedom contributes only to the Lorentz boost charge, even though it plays a role in various fluxes. The flux-balance laws are further applied to constrain the displacement memory, spin memory, and center-of-mass memory effects.