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General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
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, allowing for arbitrarily-moving sources and
observers in the presence of plane-symmetric gravitational waves. The
commonly-used predictions of linear perturbation theory are shown to be
generically overshadowed---even for very weak gravitational waves---by
nonlinear effects when considering observations of sufficiently distant
sources; higher-order perturbative corrections involve secularly-growing terms
which cannot necessarily be neglected. 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.
