The Resolution of Ambiguities in Light Perturbation by Gravitational Waves

TL;DR

This paper addresses issues in existing models of light perturbation by gravitational waves, demonstrating that pathological behaviors are due to initial data and can be fixed with improved conditions.

Contribution

It identifies the cause of pathological behaviors in light perturbation models and proposes a solution through better initial conditions.

Findings

Pathological behaviors are caused by initial or boundary data.

Improved initial conditions eliminate the pathological behavior.

The method enhances the reliability of light perturbation models.

Abstract

Some previously published expressions for the perturbation of light by gravitational waves exhibit pathological behaviour in the limit of parallel propagation. We show that this is caused by similarly pathological initial or boundary data and can thus be remedied by implementing better-behaved initial conditions.