BMS Supertranslations and Memory in Four and Higher Dimensions

TL;DR

The paper analyzes asymptotic flatness and gravitational memory in even-dimensional spacetimes, showing that the celebrated memory effect and BMS supertranslations are special to four dimensions. By using conformal Gaussian null coordinates and detailed expansions of the metric near null infinity, it demonstrates that in d>4 the leading radiation-induced changes can be removed by a gauge choice and a pure boost, effectively reducing the asymptotic symmetry group to the Poincare group. In four dimensions, the pre- and post-radiation frames differ by a nontrivial BMS supertranslation tied to the energy-momentum flux, yielding a genuine memory effect detectable via geodesic displacement. The results underscore a sharp dimensional threshold for gravitational memory and the associated asymptotic symmetry structure, with implications for conserved charges and the interpretation of gravitational radiation 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.

Theorems & Definitions (9)

• Lemma 1
• Lemma 2
• Lemma 3
• Theorem 4
• Lemma 5
• Theorem 6
• Lemma 7
• Proposition 8
• Proposition 9