Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri

The structure of polyhomogeneous space-times (i.e., space-times with metrics which admit an expansion in terms of $r^{-j}{\log }^{i}r$) constructed by a Bondi–Sachs type method is analysed. The occurrence of some log terms in an asymptotic expansion of the metric is related to the non–vanishing of the Weyl tensor at Scri. Various quantities of interest, including the Bondi mass loss formula, the peeling–off of the Riemann tensor and the Newman–Penrose constants of motion are re-examined in this context.