On asymptotic structure at null infinity in five dimensions

TL;DR

This paper defines null infinity in five-dimensional space-time using Bondi coordinates, avoiding conformal embedding due to smoothness issues in odd dimensions. It derives the asymptotic structure and mass-loss law, showing that the Bondi mass decreases due to gravitational radiation, and demonstrates that the asymptotic symmetry group at null infinity is the Poincaré group with no supertranslations. The approach identifies the five GW degrees of freedom via the C and D functions and provides explicit near-null-infinity expansions for the metric components. The results clarify the role of gravitational waves in shaping the asymptotic structure in 5D and suggest avenues for extending to higher dimensions and potential covariant conformal formulations.

Abstract

We discuss the asymptotic structure of null infinity in five dimensional space-time. Since it is known that the conformal infinity is not useful for odd higher dimensions, we shall employ the coordinate based method like the Bondi coordinate firstly introduced in four dimensions. Then we define the null infinity and identify the asymptotic symmetry. We also derive the Bondi mass expression and show its conservation law.