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Scaling and conformal symmetries for plane gravitational waves

Abstract : The isometries of an exact plane gravitational wave are symmetries for both massive and massless particles. Their conformal extensions are, in fact, chrono-projective transformations {introduced earlier by Duval et al. [Classical Quantum Gravity 3, 461 (1986); Classical Quantum Gravity 32(17), 175006 (2015)]} and are symmetries for massless particles. Homotheties are universal chrono-projective symmetries for any profile. Chrono-projective transformations also generate new conserved quantities for the underlying non-relativistic systems in the Bargmann framework. Homotheties play a similar role for the lightlike “vertical” coordinate as isometries play for the transverse coordinates.
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https://hal.archives-ouvertes.fr/hal-02144335
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Submitted on : Thursday, May 30, 2019 - 1:42:01 AM
Last modification on : Wednesday, January 13, 2021 - 4:46:06 AM

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P.-M. Zhang, M. Cariglia, M. Elbistan, P.A. Horvathy. Scaling and conformal symmetries for plane gravitational waves. J.Math.Phys., 2020, 61 (2), pp.022502. ⟨10.1063/1.5136078⟩. ⟨hal-02144335⟩

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