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.
Highlights
The advent of gravitational wave observations brings a new range of phenomena related to the dynamics of the gravitational field to our attention
We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to firstorder terms in wavelength, on arbitrary spacetime backgrounds
Following the strategy developed in Ref. [23] for the Maxwell field, as well as the general theory given in Ref. [35], we provide a derivation from first principles of effective ray equations describing the propagation of gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds
Summary
The advent of gravitational wave observations brings a new range of phenomena related to the dynamics of the gravitational field to our attention. The effective ray equations for massive spin-12 Dirac fields, beyond the geometrical optics limit, have been discussed in Refs. [35], we provide a derivation from first principles of effective ray equations describing the propagation of gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. Manifesting the spin nature of the gravitational field These corrections to the standard trajectories of geometrical optics, the null geodesics, may be termed as the spin Hall effect of gravitational waves [27]. The derivation of the spin Hall effect for gravitational waves given in Ref. [27] where the author argues that the effect is quantum in nature Another derivation of a spin Hall effect for gravitational waves was proposed in Ref. Appendix C contains a basic discussion of the Lorenz gauge
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