BMS Supertranslations and Memory in Four and Higher Dimensions

Abstract

We consider the memory effect in even dimensional spacetimes of dimension $d \ge 4$ arising from a burst of gravitational radiation. When $d=4$, the natural frames in the stationary eras before and after the burst differ by the composition of a boost and supertranslation, and this supertranslation characterizes the "memory effect," i.e., the permanent displacement of test particles near infinity produced by the radiation burst. However, we show that when $d > 4$, this supertranslation and the corresponding memory effect vanish. Consequently, when $d >4$, it is natural to impose stronger asymptotic conditions at null infinity that reduce the asymptotic symmetry group to the Poincare group. Conversely, when $d=4$, the asymptotic symmetry group at null infinity must be taken to be the BMS group.