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We calculate the scattering of two rotating objects with thelinear-in-curvature spin-induced multipoles of Kerr black holes at$\mathcal{O}(G^2)$ and all orders in the spins of both objects. This is doneincluding the complete set of contact terms potentially relevant toKerr-black-hole scattering at $\mathcal{O}(G^2)$. As such, Kerr black holesshould be described by this scattering amplitude for a specific choice ofvalues for the contact-term coefficients. The inclusion of all potentialcontact terms means this amplitude allows for a comprehensive search forstructures emerging for certain values of the coefficients, and hence specialproperties that might be exhibited by Kerr-black-hole scattering. Our resultcan also act as a template for comparison for future computations of classicalgravitational high-spin scattering.

Classical gravitational scattering at $\mathcal{O}(G^{2} S_{1}^{\infty} S_{2}^{\infty})$