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The Effective One-Body formalism of the gravitational two-body problem ingeneral relativity is reconsidered in the light of recent scattering amplitudecalculations. Based on the kinematic relationship between momenta and theeffective potential, we consider an energy-dependent effective metricdescribing the scattering in terms of an Effective One-Body problem for thereduced mass. The identification of the effective metric simplifiesconsiderably in isotropic coordinates when combined with a redefined angularmomentum map. While the effective energy-dependent metric as expected is notunique, solutions can be chosen perturbatively in the Post-Minkowskianexpansion without the need to introduce non-metric corrections. By a canonicaltransformation, our condition maps to the one based on the standard angularmomentum map. Expanding our metric around the Schwarzschild solution we recoverthe solution based on additional non-metric contributions.

Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity