Spin Hall effect of gravitational waves

TL;DR

This paper predicts a spin Hall effect for gravitational waves caused by Berry curvature, leading to trajectory splitting based on helicity, which could test quantum properties of gravitons.

Contribution

It derives the semiclassical equations of motion for gravitons incorporating Berry curvature, revealing a topological spin Hall effect unique to gravitational waves.

Findings

Gravitons exhibit Berry curvature due to helicity.

The spin Hall effect causes trajectory splitting of gravitational waves.

The effect is twice as large as that for light.

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.