Gravitational spinoptics in a curved space-time

TL;DR

This paper introduces a spinoptics approximation for high-frequency gravitational waves in curved spacetime, incorporating spin-curvature interactions via an effective action approach, simplifying analysis of gravitational wave propagation.

Contribution

It develops a covariant effective action framework for gravitational spinoptics, enabling simplified analysis of gravitational wave propagation with spin effects in arbitrary vacuum spacetimes.

Findings

Effective action reproduces known results for gravitational spinoptics.

Simplifies the study of high-frequency gravitational waves with spin.

Applicable to any vacuum spacetime background.

Abstract

In this paper we discuss propagation of the weak high-frequency gravitational waves in a curved spacetime background. We develop a so-called spinoptics approximation which takes into account interaction of the spin of the field with the curvature of the background metric. This is achieved by modifying the standard geometric optics approximation by including the helicity sensitive terms of the order $1/\omega$ in the eikonal equation. The novelty of the approach developed in this paper is that instead of study of the high-frequency expansion of the equations for the gravitational field perturbations we construct the effective action for the gravitational spinoptics. The gravitational spinoptics equations derived by variation of the effective action correctly reproduce the earlier obtained results. However, the proposed effective action approach is technically more simple and transparent. It allows one to reduce the study of the high-frequency gravitational waves to study classical dynamics of massless particles with internal discrete degree of freedom (helicity). The formalism is covariant and it can be applied for arbitrary vacuum space-time background.