Particle motion in circularly polarized vacuum pp waves

Abstract

Bialynicki-Birula and Charzynski argued that a gravitational wave emitted during the merger of a black hole binary may be approximated by a circularly polarized wave which may in turn trap particles [1]. In this paper we consider particle motion in a class of gravitational waves which includes, besides circularly polarized periodic waves (CPP) [2], also the one proposed by Lukash [3] to study anisotropic cosmological models. Both waves have a 7-parameter conformal symmetry which contains, in addition to the generic 5-parameter (broken) Carroll group, also a 6th isometry. The Lukash spacetime can be transformed by a conformal rescaling of time to a perturbed CPP problem. Bounded geodesics, found both analytically and numerically, arise when the Lukash wave is of Bianchi type VI. Their symmetries can also be derived from the Lukash-CPP relation. Particle trapping is discussed.

affiliation corrected

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• Various disguises of the Pais-Uhlenbeck oscillator
• Linearization of Newton's second law
• Displacement Memory Effect from Supersymmetry
• Conformally related vacuum gravitational waves, and their symmetries
• Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations