Helicity-dependent corrections to black-hole shadows from the gravitational spin Hall effect

Abstract: Black-hole shadows are purely geometric in the leading-order geometric-optics approximation: their boundary is set by null geodesics and carries no information about the polarization of the probing radiation. This changes at subleading order. We show that the gravitational spin Hall effect of light shifts the critical impact parameter governing photon capture by a helicity-dependent amount, causing polarized radiation with opposite helicities to trace slightly different shadow boundaries -- even in static, spherically symmetric spacetimes. The correction is analytic, universal, and scales as $1/ω$: it depends only on a single geometric function evaluated at the photon-sphere radius. We derive this result from the spin Hall equations of motion, confirm it numerically through ray-tracing calculations, and extend the analysis to Reissner-Nordström black holes, where electric charge amplifies the effect by up to a factor of $2.5$ at extremality. We further develop a perturbative treatment for slowly rotating (Kerr) spacetimes, showing that frame dragging introduces a $\cos\varphi$ modulation of the shadow splitting that can reverse its sign on one side of the image for spins $χ\gtrsim 0.21$. Although the magnitude of the effect is small, the conceptual implication is clear: black-hole shadows are not purely geometric observables.