Angular momentum at null infinity in five dimensions

TL;DR

This paper investigates the properties of angular momentum at null infinity in five-dimensional spacetimes, demonstrating the absence of supertranslational ambiguity and establishing a well-defined angular momentum framework.

Contribution

It shows that, unlike in four dimensions, angular momentum at null infinity in five dimensions is well-defined without supertranslational ambiguity due to the non-existence of supertranslations.

Findings

Angular momentum at null infinity in five dimensions is well-defined.

Supertranslational ambiguity is absent in higher dimensions.

The paper derives angular momentum loss/gain laws due to gravitational waves.

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.