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arXiv · 1612.03290

BMS Supertranslations and Memory in Four and Higher Dimensions

Stefan Hollands·Akihiro Ishibashi·Robert M. Wald
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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.

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Stefan Hollands, Akihiro Ishibashi, Robert M. Wald. 2016-12-10. BMS Supertranslations and Memory in Four and Higher Dimensions. https://doi.org/10.1088/1361-6382%2Faa777a

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