2004/07/02 by Stefan Hollands, Robert M. Wald · 4 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1088/0264-9381/21/22/008
published as Class.Quant.Grav. 21 (2004) 5139-5146 · Latex, 8 pages, no figures
arxiv created 2004/07/02 · openalex publication_date 2004/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for general relativity in odd spacetime dimensions greater than 4, all components of the unphysical Weyl tensor for arbitrary smooth, compact spatial support perturbations of Minkowski spacetime fail to be smooth at null infinity at leading nonvanishing order. This implies that for nearly flat radiating spacetimes, the non-smoothness of the unphysical metric at null infinity manifests itself at the same order as it describes deviations from flatness of the physical metric. Therefore, in odd spacetime dimensions, it does not appear that conformal null infinity can be in any way useful for describing radiation. The notion of conformal null infinity was introduced more than forty years ago by Penrose [1] in the context of 4-dimensional general relativity, and has provided a remarkably fruitful framework for giving a mathematically precise description of the asymptotic properties of gravitational radiation. In this framework, one defines an “unphysical spacetime ” with a metric that is conformally related to the physical metric, in such a way that “asymptotically large distances in null directions ” correspond to ordinary points on a boundary (“null infinity”) attached to the unphysical spacetime. One can then define notions such as Bondi mass and energy flux via local definitions on this boundary rather than by taking asymptotic limits in the original, physical spacetime. The appropriate degree of differentiability to assume for the unphysical metric has been been a subject of much discussion and analysis (see [2] and references cited therein). However, in 4-dimensional general relativity it is known that there is a wide class of radiating spacetimes for which the unphysical metric is smooth [3].