Angular momentum at null infinity in five dimensions

TL;DR

This work analyzes angular momentum at null infinity in five-dimensional asymptotically flat spacetimes using Bondi coordinates. It shows that the asymptotic symmetry group is the Poincaré group, eliminating the supertranslation ambiguities that plague the four-dimensional case, and defines a well-behaved Bondi mass and angular momentum with associated flux laws. The paper derives the Bondi mass loss law $\frac{d}{du}M_{ ext{Bondi}}= -\frac{1}{16\pi}\int_{S^3}\{(\partial_u C_{11})^2+(\partial_u C_{11})(\partial_u C_{21})+(\partial_u C_{21})^2+(\partial_u D_{11})^2+(\partial_u D_{21})^2+(\partial_u D_{31})^2\} d\Omega$ and the corresponding angular-momentum flux, and proves the Poincaré covariance of both Bondi mass and angular momentum under translations, up to radiative terms. It also discusses the finiteness of the Bondi mass, the role of gravitational waves in driving fluxes, and potential extensions to higher (and even) dimensions, noting the contrasting 4D situation where supertranslations persist. The Appendix contrasts the 4D Bondi angular momentum, highlighting the inherent supertranslation ambiguities there.

Abstract

In this paper, using the Bondi coordinates, we discuss the angular momentum at null infinity in five dimensions and address the Poincare covariance of the Bondi mass and angular momentum. We also show the angular momentum loss/gain law due to gravitational waves. In four dimensions, the angular momentum at null infinity has the supertranslational ambiguity and then it is known that we cannot construct well-defined angular momentum there. On the other hand, we would stress that we can define angular momentum at null infinity without any ambiguity in higher dimensions. This is because of the non-existence of supertranslations in higher dimensions.