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2018_EJRNL_PP_CLIFFORD_CHEUNG_1.pdf
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We combine tools from effective field theory and generalized unitarity to construct a map between onshell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.