Optics in a nonlinear gravitational plane wave

TL;DR

This paper derives exact expressions for gravitational lensing effects caused by plane-symmetric gravitational waves in general relativity, revealing significant nonlinear effects that can overshadow linear predictions and mimic additional polarization modes.

Contribution

It provides the first exact formulas for lensing by nonlinear gravitational waves, highlighting the importance of nonlinear effects in astrophysical observations.

Findings

Nonlinear effects can dominate linear predictions even for weak waves.

Higher-order perturbations involve secular growth, affecting distant source observations.

Nonlinear corrections can mimic a third polarization mode of gravitational waves.

Abstract

Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.