Approximate models for gravitational memory

Abstract

The large-distance approximation of a sandwich gravitational wave by a continuous but not necessarily smooth profile provides us with an approximate analytic description of particle motion in a gravitational wave as spelled out for the P & ouml;schl-Teller profile. Displacement Memory is obtained by fine-tuning the amplitude. The role of the 2nd solution of the Sturm-Liouville equation is highlighted. Similar results hold for a Gaussian and simple square profiles. Our approximate models are consistent with Carroll symmetry.