Smoothness at null infinity and the structure of initial data

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We describe our present understanding of the relations between the behaviour of asymptotically flat Cauchy data for Einstein's vacuum field equations near space-like infinity and the asymptotic behaviour of their evolution in time at null infinity.
86 pages, typo corrected and largely extended version of earlier article, to appear in the volume "50 years of the Cauchy problem in general relativity"

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