More on gravitational memory

TL;DR

The paper addresses how gravitational memory phenomena extend to spacetimes with nonstandard boundary topology by employing Weyl transformations to map to the unit $S^2$ and derive a generalized displacement memory encoded in the Weyl-invariant shear, with explicit Robinson-Trautman examples. It also introduces a novel spin-memory observable as a time delay for time-like free-falling observers at large radius, linking this delay to angular-momentum flux and NP data. Additionally, it shows that conjugate points along asymptotic time-like geodesics are far apart, reducing near-field obstructions to memory measurements, and situates these results within the broader context of soft graviton theorems and BMS$_4$ symmetries. Overall, the work provides new theoretical tools and observational pathways for gravitational memory, bridging exact solutions, boundary topology, and asymptotic symmetries.

Abstract

Two novel results for the gravitational memory effect are presented in this paper. We first extend the formula for the memory effect to solutions with arbitrary two surface boundary topology. The memory effect for the Robinson-Trautman solution is obtained in its standard form. Then we propose a new observational effect for the spin memory. It is a time delay of time-like free falling observers.