Post-Minkowskian Scattering Angle in Einstein Gravity

TL;DR

This paper derives a universal, simple formula for the relativistic two-body scattering angle in Einstein gravity using the post-Minkowskian expansion, linking the amplitude directly to the scattering outcome.

Contribution

It establishes a one-to-one correspondence between solutions of the relativistic Lippmann-Schwinger equation and the energy equation, enabling direct computation of the scattering angle from the amplitude.

Findings

Scattering angle can be obtained directly from the amplitude.

Provides a universal formula valid to any order in post-Minkowskian expansion.

Simplifies calculations in Einstein gravity for relativistic two-body scattering.

Abstract

Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.