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

TL;DR

This paper analyzes the structure of polyhomogeneous space-times in general relativity, focusing on Bondi expansions and the implications of log terms in asymptotic metrics related to gravitational radiation and conserved quantities.

Contribution

It provides a detailed analysis of polyhomogeneous space-times using Bondi--Sachs methods, linking log terms in asymptotic expansions to the Weyl tensor at Scri and revisiting key gravitational quantities.

Findings

Log terms in metric expansions relate to non-zero Weyl tensor at Scri.

Re-examination of Bondi mass loss and peeling properties in polyhomogeneous space-times.

Clarification of Newman--Penrose constants in the context of polyhomogeneity.

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.