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 Möbius 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.

中文翻译：

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引力平面波的位移与速度记忆效应


本文证明，除了众所周知的速度记忆效应之外，真空引力平面波还可以在几个测试粒子上引起位移记忆。建立了速度或位移记忆效应发生条件的完整分类。这些条件取决于相对运动的初始条件和波廓。处理波允许脉冲或阶跃轮廓的两种情况。然后，我们的解析表达式与数值积分进行比较，以显示速度或位移记忆（在这两个剖面系列的情况下）。除了这种分类之外，还证明了在零时间莫比乌斯重新参数化下存在偏振真空引力平面波的新对称性。最后，我们利用真空引力平面波的基本对称性讨论了测地偏差方程的求解。