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. At subleading order, the gravitational spin Hall effect of light introduces helicity-dependent corrections to photon propagation. We show that, in any static spherically symmetric spacetime, an exact equatorial reflection symmetry of the full spin Hall equations forces these corrections to cancel at the capture threshold: the critical impact parameter remains identical for opposite helicities, and no polarization-dependent shadow splitting occurs. Rotation breaks this symmetry. Using a double perturbative expansion in the black-hole spin $χ= a/M$ and in the inverse frequency $1/ω$, we derive the first non-vanishing helicity-dependent shift of the critical impact parameter for slowly rotating (Kerr) black holes. The effect is linear in $χ$, scales as $1/ω$, and appears as a $\cosϕ$ modulation of the shadow boundary, with a sign reversal on one side of the image for spins $χ\gtrsim 0.21$. Although parametrically small for astrophysical sources, the splitting is a robust, model-independent signature of spin-optical dynamics in strong fields. Our analysis also identifies a methodological pitfall: a naive radial projection that suppresses transverse motion can produce a spurious splitting even in spherical symmetry, a lesson of general relevance for future studies of spin-optical effects.