On Post-Minkowskian Hamiltonians in General Relativity

Abstract: We describe the computation of post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical General Relativity to any order in Newton's constant. We illustrate this by deriving an Hamiltonian for binary black holes without spin up to 2nd order in the post-Minkowskian expansion and demonstrate explicitly the equivalence with the recently proposed method based on an effective field theory matching.