From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

TL;DR

This paper develops a method combining effective field theory and unitarity to derive classical gravitational potentials from scattering amplitudes, successfully matching known results up to 4PN order and enabling future higher-order calculations.

Contribution

It introduces a novel approach linking on-shell amplitudes to classical potentials, providing analytic expressions for binary black holes at second order in G and all velocities.

Findings

Derived classical potential at second order in G for binary black holes

Matched all known results up to 4PN order

Provided a framework for extending to higher orders

Abstract

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.