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Gravity is the curvature of spacetime, not just an attraction, as Einstein showed. On such a curved "dance floor", even the hypothetical carriers of gravity — gravitons — move oddly. Like dancers spinning right and left, the floor's curvature makes them drift in opposite directions. This is a geometric shift, rooted in the

For light (photons), such spin-dependent separation is already known. But gravitons have double the spin (spin 2), so the effect is twice as noticeable. In the strong field of a black hole, right- and left-handed gravitons will diverge far apart. Catching this separation could allow us to detect individual quanta of gravity for the first time. By the way, the Berry curvature itself was discovered by Michael Berry in molecular systems — the very twist that now points to the quantum nature of gravity.

Original abstract

as written by the authors arXiv:2605.19817

Based on quantum field theory of linearized gravity, we formulate the Wigner function for right- and left-handed gravitons. By applying the Wigner transformation to the second-order metric perturbations in the graviton energy-momentum tensor obtained from the Einstein-Hilbert action, we demonstrate the emergence of the spin Hall effect of gravitons in curved spacetime. This effect originates from the Berry curvature of gravitons, which has opposite signs for right- and left-handed helicities, and leads to a helicity-dependent splitting of the graviton energy Hall current. The magnitude of this splitting is found to be exactly twice that of the corresponding spin Hall current for photons.