Gravitational Faraday effect from on-shell amplitudes

Effects of massive object's spin on massive-massless $2 \to 2$ classical
scattering is studied. Focus is set on the less-considered dimensionless
expansion parameter $\lambda/b$, where $\lambda$ is the massless particle's
wavelength and $b$ is the impact parameter. Corrections in $\lambda/b$ start to
appear from $\mathcal{O}(G^2)$, with leading correction terms tied to the
gravitational Faraday effect, which is a special case of the Lense-Thirring
effect. We compute the eikonal phase up to $\mathcal{O}(G^2)$ and extract spin
effect on the scattering angle and time delay up to 14th order in spin. The
gravitational Faraday effect at linear order in spin is reproduced by
$\lambda/b$ correction terms, which we compute to higher orders in spin. We
find that the equivalence principle, or universality, holds up to NLO for
general spinning bodies, i.e. away from geometric optics limit. Furthermore, in
the black hole limit, we confirm the absence of particular spin structure
observed, along with the associated shift symmetry, and argue that it holds to
arbitrary spin order at $\mathcal{O}(G^2)$ in the massless probe limit.