Radiative gravitational fields in general relativity II. Asymptotic behaviour at future null infinity

We prove that Penrose's requirements for asymptotic simplicity are formally satisfied by the general metric, (1), which admits both post-Minkowskian and multipolar expansions, (2), which is stationary in the past and asymptotically Minkowskian in the past, (3), which admits harmonic coordinates, and (4), which is a solution of Einstein's vacuum equations outside a spatially bounded region. The proof is based on the setting up, by using the method of a previous work (L. Blanchet & T. Damour (Phil. Trans. R. Soc. Lond. A 320, 379-430 (1986))), of an improved algorithm that generates a metric equivalent to the general harmonic metric of that work but written in radiative coordinates, i.e. admitting an expansion in powers of $r^{-1}$ for $r\rightarrow \infty$ and $t - r$ fixed. The arbitrary parameters of the construction are the radiative multipole moments in the sense of K. S. Thorne (Rev. mod. Phys. 52, 299 (1980)).