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

TL;DR

This paper revisits the Effective One-Body formalism in general relativity for two-body scattering, proposing a simplified, energy-dependent effective metric approach aligned with recent amplitude calculations, and explores its perturbative solutions.

Contribution

It introduces a new formulation of the EOB formalism using an energy-dependent effective metric, simplifying the approach and connecting it with recent scattering amplitude results.

Findings

Recovered known Schwarzschild solution as a special case

Simplified the effective metric in isotropic coordinates

Established a perturbative framework in Post-Minkowskian expansion

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.