Propagation of polarized gravitational waves

TL;DR

This paper derives covariant equations describing how polarized high-frequency gravitational waves propagate through curved spacetime, revealing polarization-dependent effects similar to the gravitational spin Hall effect of light.

Contribution

It provides the first covariant derivation of effective ray equations for polarized gravitational waves, including first-order wavelength corrections on arbitrary backgrounds.

Findings

Polarization-dependent modifications to gravitational wave propagation.

Effective ray equations resemble those for light's gravitational spin Hall effect.

First-order wavelength effects are significant for high-frequency gravitational waves.

Abstract

The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of gravitational waves via a spin-orbit coupling mechanism. We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. The effective ray equations describe a gravitational spin Hall effect for gravitational waves and are of the same form as those describing the gravitational spin Hall effect of light, derived from Maxwell's equations.