  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.
