Spin angular momentum of gravitational wave interference

Abstract

Spin angular momentum (SAM) is an important feature for wave systems, prominent in various properties like spin-momentum locking of wave propagations. Here, we study the SAM of gravitational waves in general relativity based on the Noether theorem in classical field theory. We demonstrate gravitational wave spin in various interference cases and evanescent waves, which is manifested as locally rotating metric perturbations, driving particles on geodesic spheroid locally deformed in elliptical trajectories. For non-polarized gravitational wave modes of zero SAM, their superpositions can induce nonzero density of SAM with interfered patterns. The evanescent gravitational wave shows clear SAM, which is also a consequence of wave interference between propagating and transverse evanescent components. The spin-momentum locking relations are clearly present for all different interference cases of wave modes and components based on general relativity.