Asymptotic behavior of null geodesics near future null infinity: Significance of gravitational waves

TL;DR

This paper studies how null geodesics behave near future null infinity in asymptotically flat spacetimes, highlighting the role of gravitational waves and differences between four and higher dimensions.

Contribution

It provides a detailed analysis of null geodesic asymptotics in various dimensions, emphasizing the impact of gravitational waves on their reachability of null infinity.

Findings

In four dimensions, gravitational waves can prevent photons from reaching null infinity without additional assumptions.

In higher dimensions, gravitational waves do not hinder null geodesics from reaching null infinity.

Different conditions are required for null geodesics to reach infinity in four versus higher dimensions.

Abstract

We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in the directions tangential to the constant radial surfaces in the Bondi coordinates. The analysis is performed for general dimensions, and the difference between the four-dimensional cases and the higher-dimensional cases is stressed. In four dimensions, some assumptions are required to guarantee the null geodesics to reach future null infinity, in addition to the conditions of asymptotic flatness. Without these assumptions, gravitational waves may prevent photons from reaching null infinity. In higher dimensions, by contrast, such assumptions are not necessary, and gravitational waves do not affect the asymptotic behavior of null geodesics.