Memory effect for particle scattering in odd spacetime dimensions

Abstract

We investigate the gravitational memory effect for linearized perturbations off of Minkowski space in odd spacetime dimensions $d$ by examining the effects of gravitational radiation from classical point particle scattering. We also investigate analogous memory effects for electromagnetic and scalar radiation. We find that there is no gravitational memory effect in all odd dimensions. For scalar and electromagnetic fields, there is no memory effect for $d\ensuremath{\ge}7$; for $d=3$ there is an infinite momentum memory effect, whereas for $d=5$ there is no momentum memory effect but the displacement of a test particle will grow unboundedly with time. Our results are further elucidated by analyzing the memory effect for any slowly moving source of compact spatial support in odd dimensions.