The Memory Effect for Particle Scattering in Even Spacetime Dimensions

TL;DR

The paper analyzes the gravitational memory effect for classical point-particle scattering in linearized gravity on $d$-dimensional Minkowski space, focusing on even $d$. It derives the retarded-field solutions for scalar, electromagnetic, and gravitational perturbations and shows memory is tied to derivatives of $ ext{Θ}(U)$ with respect to the retarded time $U=t-r$. It demonstrates that memory exists in $d=4$ but vanishes for all even dimensions with $d>4$, in agreement with Hollands–Ishibashi–Wald, and it clarifies this via a slow-motion analysis where leading radiation scales with monopole, dipole, and quadrupole moments. These results illuminate how the dimension controls memory through the structure of the leading curvature and its effect on geodesic deviation and test-particle displacement.

Abstract

We explicitly calculate the gravitational wave memory effect for classical point particle sources in linearized gravity off of an even dimensional Minkowski background. We show that there is no memory effect in $d>4$ dimensions, in agreement with the general analysis of Hollands, Ishibashi, and Wald (2016).