Gravitational waves in general relativity XIV. Bondi expansions and the ‘polyhomogeneity’ of ℐ

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 ℐ. The validity in this more general context of various results from the standard treat­ment of ℐ, including the Bondi mass loss formula, the peeling-off of the Riemann tensor and the Newman-Penrose constants of motion, is considered.