Approximate Models for Gravitational Memory

TL;DR

This paper presents approximate analytical models for gravitational waves with different profiles, demonstrating their effectiveness in describing particle motion and highlighting the role of Sturm-Liouville solutions, consistent with Carroll symmetry.

Contribution

It introduces approximate models for gravitational waves with various profiles, emphasizing the role of Sturm-Liouville solutions and Carroll symmetry in the analysis.

Findings

Analytic description of particle motion in Pöschl-Teller profile gravitational waves.

Approximate models work well for Gaussian and square profiles.

Models are consistent with Carroll symmetry.

Abstract

The large-distance approximation of a sandwich gravitational wave by a continuos but not necessarily smooth profile provides us with a surprisingly good analytic description of particle motion in a gravitational wave with P\"oschl-Teller profile. The role of the 2nd solution of the Sturm-Liouville equation is highlighted. Similar results hold for Gaussian and square profiles. Our approximate models are consistent with Carroll symmetry.