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

Abstract

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.