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arXiv · 2406.07106

Displacement versus velocity memory effects from a gravitational plane wave

Jibril Ben Achour·Jean-Philippe Uzan
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Abstract

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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Jibril Ben Achour, Jean-Philippe Uzan. 2024-06-11. Displacement versus velocity memory effects from a gravitational plane wave. https://arxiv.org/abs/2406.07106

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