  By exploiting the Kerr-Schild gauge, we study the scattering of a massive
(charged) scalar off a Kerr-Newman black hole. In this gauge, the interactions
between the probe and the target involve only tri-linear vertices. We manage to
write down the tree-level scattering amplitudes in analytic form, from which we
can construct an expression for the eikonal phase which is exact in the spin of
the black hole at arbitrary order in the Post-Minkowskian expansion. We compute
the classical contribution to the cross-section and deflection angle at leading
order for a Kerr black hole for arbitrary orientation of the spin. Finally, we
test our method by reproducing the classical amplitude for a Schwarzschild
black hole at second Post-Minkowskian order and outline how to extend the
analysis to the Kerr-Newman case.
