Modifications to Plane Gravitational Waves from Minimal Lorentz Violation

TL;DR

This paper investigates how minimal Lorentz violation alters the properties and effects of plane gravitational waves predicted by General Relativity, using perturbation theory to analyze modifications and test particle motions.

Contribution

It provides a first-order perturbative analysis of gravitational wave modifications due to minimal Lorentz violation and explores their impact on test particle trajectories.

Findings

First-order metric perturbations due to Lorentz violation are derived.

Test particle motions show measurable deviations from standard predictions.

The study offers insights into potential observational signatures of Lorentz violation in gravitational waves.

Abstract

General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found.