Asymptotic flatness at null infinity in arbitrary dimensions

TL;DR

This paper generalizes the concept of asymptotic flatness and analyzes asymptotic symmetries at null infinity across arbitrary dimensions, providing a framework for understanding gravitational fields and mass loss in higher-dimensional spacetimes.

Contribution

It introduces a new definition of asymptotic flatness and symmetry at null infinity applicable to any number of dimensions, extending previous four-dimensional results.

Findings

Defined asymptotic flatness in arbitrary dimensions

Established asymptotic symmetry and Bondi mass loss law in higher dimensions

Solved Einstein equations to analyze gravitational field behavior

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.