Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions

Details Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions

2004-07-02

arxiv.org/abs/gr-qc/0407014v1

Class.Quant.Grav. 21 (2004) 5139-5146

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 8 pages, no figures

Scientific paper

10.1088/0264-9381/21/22/008

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.

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