1. Sebastian J. Szybka, Syed U. Naqvi
Chaos and Einstein-Rosen gravitational waves
Phys. Rev. D: Part. Fields , vol. 108, p. L081501 (2023).
[abstract] [preprint] [journal] [arXiv]

Abstract:
We demonstrate the existence of chaotic geodesics for the Einstein-Rosen standing gravitational waves. The complex dynamics of massive test particles are governed by a chaotic heteroclinic network. We present the fractal associated with the system under investigation. Gravitational standing waves produce intricate patterns through test particles in a vague analogy to mechanical vibrations generating Chladni figures and complicated shapes of Faraday waves.

2. Sebastian J. Szybka, Syed U. Naqvi
Freely falling bodies in a standing-wave spacetime
Phys. Rev. D: Part. Fields , vol. 103, p. 024011 (2021).
[abstract] [preprint] [journal] [pdf]

Abstract:
We study the motion of free masses subject to the influence of standing gravitational waves in the polarized Gowdy cosmology with a three-torus topology. We show that antinodes attract freely falling particles and we trace the velocity memory effect.