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    Globally defined Carroll symmetry of gravitational waves
    (Elsevier, 2026) Elbistan, M.; Zhang, P. M.; Horvathy, P. A.
    The local Carroll symmetry of a gravitational wave found in Baldwin-Jeffery-Rosen coordinates is extended to a globally defined one by switching to Brinkmann coordinates. Two independent globally defined solutions of a Sturm-Liouville equation allow us to describe both the symmetries (translations and Carroll boosts) and the geodesic motions. One of them satisfies particular initial conditions which imply zero initial momentum, while the other does not. Pure displacement arises when the latter is turned off by requiring the momentum to vanish and when the wave parameters take, in addition, some particular values which correspond to having an integer half-wave number. The relation to the Schwarzian derivative is highlighted. We illustrate our general statements by the P & ouml;schl-Teller profile.
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    Gravitational wave memory: Further examples
    (World Scientific Publ Co Pte Ltd, 2026) Zhao, Q. -L; Zhang, P. -M; Elbistan, M.; Horvathy, P. A.
    Ehlers and Kundt [J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, New York, 1962)] argued in favor of the velocity effect: particles initially at rest hit by a burst of gravitational waves should fly apart with constant velocity after the wave has passed. Zel'dovich and Polnarev [Y. B. Zel'dovich and A. G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Astron. Zh. 51 (1974) 30, [Sov. Astron. 18 (1974) 17]] suggested instead that waves generated by flyby would merely displace the particles, as illustrated here by further examples.