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

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