On the polarization of nonlinear gravitational waves

TL;DR

This paper explores how nonlinear effects in Einstein's equations cause gravitational waves to lose their simple polarization states, indicating real waves may differ from linear predictions used in detectors.

Contribution

It derives a relation between polarization modes of nonlinear gravitational waves, showing their non-independence and impact on wave behavior.

Findings

Nonlinear gravitational waves have coupled polarization modes.

Monochromatic waves lose periodicity due to nonlinearity.

Real gravitational waves may differ from linearized solutions.

Abstract

We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.