General Relativity from Scattering Amplitudes

TL;DR

This paper applies modern quantum field theory techniques to classical general relativity, calculating interaction potentials and scattering functions for massive objects, simplifying complex calculations through unitarity cuts, and deriving exact results for light-by-light scattering.

Contribution

It introduces a quantum field theoretic approach to classical gravity, enabling systematic calculations of gravitational interactions using scattering amplitudes.

Findings

Computed interaction potentials to second order in post-Newtonian expansion.

Derived scattering functions for two massive objects to second order in post-Minkowskian expansion.

Obtained an all-order exact result for gravitational light-by-light scattering.

Abstract

We outline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multi-graviton two-body on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to non-analytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.