Memory Effect for Particle Scattering in Odd Spacetime Dimensions

TL;DR

This paper examines gravitational, electromagnetic, and scalar memory effects in odd-dimensional spacetimes, finding no gravitational memory and dimension-dependent electromagnetic and scalar effects, with detailed analysis for slowly moving sources.

Contribution

It provides a comprehensive analysis of memory effects in odd dimensions, revealing the absence of gravitational memory and dimension-specific electromagnetic and scalar memory behaviors.

Findings

No gravitational memory in all odd dimensions.

Electromagnetic and scalar memory effects depend on the dimension, with specific behaviors at d=3, 5, and ≥7.

Displacement of test particles can grow unboundedly in certain scalar cases.

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 $d\geq 7$; 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.