Particle motion in circularly polarized vacuum pp waves

TL;DR

This paper investigates particle trajectories in specific gravitational wave spacetimes, revealing conditions for particle trapping and analyzing symmetries, with implications for understanding gravitational wave interactions with matter.

Contribution

It introduces a unified analysis of particle motion in circularly polarized and Lukash gravitational waves, highlighting conformal symmetries and particle trapping mechanisms.

Findings

Bound geodesics exist in Bianchi type VI Lukash waves

Conformal symmetries relate Lukash and CPP spacetimes

Particle trapping occurs under specific wave conditions

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.