On the motion of spinning test particles in plane gravitational waves

TL;DR

This paper analyzes the motion of spinning test particles in plane gravitational waves, deriving explicit solutions and revealing phenomena like parametric excitation, with implications for understanding particle-wave interactions in general relativity.

Contribution

It provides explicit solutions to the Mathisson-Papapetrou-Dixon equations in plane gravitational waves, including reduction to Mathieu-Hill type equations for harmonic waves, and explores scattering effects.

Findings

Spinning particles can undergo parametric excitation in gravitational waves.

Explicit solutions are constructed using linear differential equations.

The particle's final energy depends on wave properties and spin orientation.

Abstract

The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle in plane gravitational waves are analysed and explicit solutions constructed in terms of solutions of certain linear ordinary differential equations. For harmonic waves this system reduces to a single equation of Mathieu-Hill type. In this case spinning particles may exhibit parametric excitation by gravitational fields. For a spinning test particle scattered by a gravitational wave pulse, the final energy-momentum of the particle may be related to the width, height, polarisation of the wave and spin orientation of the particle.