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

TL;DR

In odd spacetime dimensions greater than four, conformal null infinity cannot be used to describe radiation due to the non-smoothness of the unphysical Weyl tensor at null infinity.

Contribution

This paper demonstrates that conformal null infinity does not exist for radiating solutions in odd spacetime dimensions greater than four.

Findings

Unphysical Weyl tensor components are not smooth at null infinity in odd dimensions.

Non-smoothness appears at the same order as deviations from flatness.

Conformal null infinity is not useful for describing radiation in these dimensions.

Abstract

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.