Title: Spin Hall effect of gravitational waves,
Abstract: Gravitons possess a Berry curvature due to their helicity. We derive the
semiclassical equations of motion for gravitons taking into account the Berry
curvature. We show that this quantum correction leads to the splitting of the
trajectories of right- and left-handed gravitational waves in curved space, and
that this correction can be understood as a topological phenomenon. This is the
spin Hall effect (SHE) of gravitational waves. We find that the SHE of
gravitational waves is twice as large as that of light. Possible future
observations of the SHE of gravitational waves can potentially test the quantum
nature of gravitons beyond the classical general relativity.