Examination of a simple example of gravitational wave memory

TL;DR

The paper analyzes gravitational-wave memory in a simple decay process $M \to E$ (null) + recoiling $M'$ and generalizes to two timelike products, clarifying the distinction between null memory and ordinary memory. It uses the twmemory approach to derive explicit expressions for the memory displacement $\Delta D_a$ and decomposes memory into ordinary ($\Delta P$) and null ($F$) components, comparing with the Lydia–Me formalism. The null-decay result shows memory is entirely null to leading order in $E/M$, while the timelike-decay case yields ordinary memory that, in the limit $\beta\to 1$, converges to the null-memory profile via a distributional contribution from $\Delta P_E$; this demonstrates how ordinary memory can imitate null memory at high speeds. Overall, the total memory equals the sum of ordinary and null parts, with the null limit recovered in the timelike-to-null transition, illustrating the interplay between decay dynamics and memory in linearized gravity.

Abstract

We examine a simple example of gravitational wave memory due to the decay of a point particle into two point particles. In the case where one of the decay products is null, there are two types of memory: a null memory due to the null particle and an ordinary memory due to the recoiling timelike particle. In the case where both decay products are timelike, there is only ordinary memory. However, this ordinary memory can mimic the null memory in the limit where one of the decay products has a large velocity.