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Displacement versus velocity memory effects from a gravitational plane wave

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arxiv 2406.07106 v2 pith:DZVAPTTJ submitted 2024-06-11 gr-qc hep-th

Jibril Ben Achour , Jean-Philippe Uzan This is my paper · ORCID
classification gr-qchep-th
keywords wavememorydisplacementgravitationalplanevelocityconditionsvacuum
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This article demonstrates that additionally to the well-known velocity memory effect, a vacuum gravitational plane wave can also induce a displacement memory on a couple of test particles. A complete classification of the conditions under which a velocity or a displacement memory effect occur is established. These conditions depend both the initial conditions of the relative motion and on the wave profile. The two cases where the wave admits a pulse or a step profile are treated. Our analytical expressions are then compared to numerical integrations to exhibit either a velocity or a displacement memory, in the case of these two families of profiles. Additionally to this classification, the existence of a new symmetry of polarized vacuum gravitational plane wave under M\"{o}bius reparametrization of the null time is demonstrated. Finally, we discuss the resolution of the geodesic deviation equation by means of the underlying symmetries of vacuum gravitational plane wave.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Flyby-induced displacement: analytic solution

    gr-qc 2025-02 accept novelty 5.0 of 10

    The authors derive exact analytic solutions for gravitational wave displacement memory when the flyby profile is approximated by the hyperbolic Scarf potential, with magic amplitude values |g|=(2n+1) sqrt(n(n+1)).

  2. Memory Effect for deformed gravitational waves

    gr-qc 2026-07 conditional novelty 4.0 of 10

    Displacement memory in squeezed Pöschl–Teller gravitational waves is lost in the finite-amplitude impulsive limit; restoring it requires amplitudes that diverge as the squeezing parameter p→∞.

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