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We revisit the problem of flux-balance equations for isolated post-Newtonianmatter systems due to the emission of gravitational waves. In particular weshow by a local derivation confined to the system, using the expression ofradiation-reaction forces up to the 3.5PN order, that not only the energy,angular momentum and linear momentum of the system, but also the position ofits center of mass, obey some (non-trivial) flux-balance equations. The balanceequation for the center-of-mass position completes the description of thesecular evolution by gravitational waves of relativistic post-Newtonianisolated matter systems. We then confirm this result by a direct computation ofthe gravitational-wave fluxes at future null infinity, obtaining the fullmultipole-moment expansion of the flux associated with the center-of-massposition (probably new with this paper), and rederiving as well the knownmultipole-moment expansions of the fluxes of energy, angular momentum andlinear momentum. We also check our analysis by a direct calculation ofradiation-reaction effects in the case of compact binary systems.

Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems