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

Abstract

The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations. Based on the kinematic relationship between momenta and the effective potential, we consider an energy-dependent effective metric describing the scattering in terms of an Effective One-Body problem for the reduced mass. The identification of the effective metric simplifies considerably in isotropic coordinates when combined with a redefined angular momentum map. While the effective energy-dependent metric as expected is not unique, solutions can be chosen perturbatively in the Post-Minkowskian expansion without the need to introduce non-metric corrections. By a canonical transformation, our condition maps to the one based on the standard angular momentum map. Expanding our metric around the Schwarzschild solution we recover the solution based on additional non-metric contributions.

10 pages. v3: stylistic corrections, version matching the published version in PRD

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• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Scattering Angles in Kerr Metrics
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• The Radial Action from Probe Amplitudes to All Orders
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework