Classical Spinning Black Hole Scattering from Quantum Amplitudes

Scattering amplitudes have recently become a powerful tool for extracting classical observables in two-body gravitational dynamics, with direct relevance for current and future gravitational-wave experiments. In this talk, I will review how quantum scattering amplitudes can be used to obtain classical black hole scattering observables. A key focus will be the inclusion of spin effects, modelled by treating black holes as point particles in fixed-spin representations. This approach introduces a subtle ambiguity in the separation between classical and quantum information, which we resolve using our spin interpolation method. Leveraging this, we obtain, for the first time, the classical two-loop amplitude accurate to quartic order in spin, from which we extract physical observables such as linear and angular impulses using covariant Dirac brackets. Remarkably, the resulting amplitude obeys a spin-shift symmetry, remaining invariant under a shift of the black hole spin by the momentum transfer in the scattering process. Motivated by this structure, we examine the conserved quantities governing scattering and show that—at least asymptotically—the probe dynamics remain integrable through quartic order in spin. Under this asymptotic integrability, together with the spin-shift symmetry, we demonstrate that the quartic-in-spin radial action is fully determined by the aligned-spin sector. Taken together, these results advance our understanding of spinning black hole scattering and illuminate new structural features of Kerr dynamics.