General Relativity from Scattering Amplitudes

TL;DR

The paper shows that classical general relativity emerges from quantum scattering amplitudes by retaining only the long-distance, non-analytic pieces of loop amplitudes via unitarity cuts. It develops a relativistic, two-body scattering program in which the post-Newtonian and post-Minkowskian dynamics are obtained from triangle-topology contributions and eikonal exponentiation, respectively, with kinematic definitions $M^2 = s$ and $\hat M^2 = M^2 - m_1^2 - m_2^2$ and the eikonal relation $M(\vec{b}) \sim 4p(E_1+E_2)(e^{i\chi(\vec{b})}-1)$. It reports explicit results for scalar-scalar interactions to second order in both PN and PM, and derives an all-order, exact result for gravitational light-by-light scattering, highlighting a unifying, efficient framework for gravity as an EFT. The approach promises scalable routes to higher-derivative gravitational couplings and could impact gravitational-wave modelling and tests of GR.

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.