Gravitational Waveforms from Scattering Amplitudes

The synergy between amplitude based and general relativity based perturbation methods has led to many interesting new insights on gravitational two-body systems. I will present the recent computation of the scattering waveform at O(G²) and all order in the relative velocity, using the amplitude based KMOC formalism. To achieve the correct result, one needs to carefully take into account several subtle contributions: (1) the iterative part of the KMOC matrix elements, which is intimately correlated with a frame choice; (2) the scheme dependent epsilon/epsilon contribution from the dimensional regularization of the IR divergence; (3) both the external and internal zero-energy gravitons whose contribution turns out to be a BMS transformation. We find exact agreement up to 2.5PN with the waveform computed from the general relativity based MPM method.