# Deviation and precession effects in the field of a weak gravitational wave

## TL;DR

This paper investigates how weak gravitational plane waves influence spinning particles, causing deviation and precession effects, with solutions provided for deviation and spin transport equations in a laboratory frame.

## Contribution

It extends the MPD model off the particle's world line and derives an exact transformation between TT and Fermi coordinates for measurable analysis.

## Key findings

- Particles move on a 2-plane orthogonal to wave propagation
- Transverse spin vectors oscillate around initial orientation
- Exact TT to Fermi coordinate transformation derived

## Abstract

Deviation and precession effects of a bunch of spinning particles in the field of a weak gravitational plane wave are studied according to the Mathisson-Papapetrou-Dixon (MPD) model. Before the passage of the wave the particles are at rest with associated spin vector aligned along a given direction with constant magnitude. The interaction with the gravitational wave causes the particles to keep moving on the 2-plane orthogonal to the direction of propagation of the wave, with the transverse spin vector undergoing oscillations around the initial orientation. The transport equations for both the deviation vector an spin vector between two neighboring world lines of such a congruence are then solved by a suitable extension of the MPD model off the spinning particle's world line. In order obtain measurable physical quantities a "laboratory" has been set up by constructing a Fermi coordinate system attached to a reference world line. The {\it exact} transformation between TT coordinates and Fermi coordinates is derived too.