BMS supertranslations and memory in four and higher dimensions

We consider the memory effect in even dimensional spacetimes of dimension d >= 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.