Asymptotic flatness at null infinity in arbitrary dimensions

TL;DR

This work extends the study of asymptotic flatness to null infinity in arbitrary dimensions using Bondi coordinates. By solving vacuum Einstein equations in this setting, it defines precise fall-off conditions, proves the finiteness of the Bondi mass, and derives a Bondi mass loss law driven by gravitational radiation. It further shows that the asymptotic symmetry group is the Poincaré group in higher dimensions (with 4D allowing supertranslations) and demonstrates Poincaré covariance of the Bondi energy-momentum under these transformations. The results generalize known even-dimensional analyses and set the stage for including angular momentum in future higher-dimensional investigations.

Abstract

We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior of gravitational fields. Then we show the asymptotic symmetry and the Bondi mass loss law with the well-defined definition.