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.
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