Schwarzschild geodesics from Scattering Amplitudes to all orders in $G_N$

TL;DR

This paper derives the geodesic motion of a light body in a Schwarzschild background at leading self-force order using scattering amplitudes, providing a novel flat space approach to black hole dynamics.

Contribution

It introduces a new method to compute Schwarzschild geodesics from scattering amplitudes at all orders in Newton's constant.

Findings

Explicit derivation of 0SF geodesics using scattering amplitudes

Utilization of cubic Einstein gravity coupled to worldline action

Connection to previous Schwarzschild metric derivation

Abstract

The dynamics of the leading self-force (0SF) order, corresponding to the geodesic motion of a light body in the exact background of a heavy body, are explicitly derived for the first time using a flat space scattering amplitude-based approach. This is achieved by utilising the cubic formulation of Einstein's general relativity coupled to the effective worldline action of massive point particles, which was employed to derive the Schwarzschild black hole metric in arXiv:2405.14421.