Radiative Gravitation Fields in General Relativity II. Asymptotic Behaviour at Future Null Infinity

Physics

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Scientific paper

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--> ∞ 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)).

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