BMS Supertranslations and Memory in Four and Higher Dimensions

TL;DR

This paper investigates gravitational memory effects in higher-dimensional spacetimes, finding that such effects and supertranslations are present only in four dimensions, leading to different asymptotic symmetry groups.

Contribution

It demonstrates that supertranslations and memory effects vanish in dimensions greater than four, suggesting a stronger asymptotic symmetry group in higher dimensions.

Findings

Memory effect exists only in 4D spacetimes.

Supertranslations vanish for dimensions greater than 4.

Asymptotic symmetry group reduces to Poincare in 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.