The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

TL;DR

This review explores how scattering amplitudes from quantum field theory can be applied to classical gravity, enabling new insights into gravitational phenomena and solutions through the double copy formalism.

Contribution

It introduces a formalism linking classical observables to scattering amplitudes and extends the classical double copy to exact solutions in gravity.

Findings

Connection between scattering amplitudes and classical gravitational observables.

Application of the double copy to classical solutions in gravity.

Extension of the classical double copy from linearised to exact solutions.

Abstract

Scattering amplitudes have their origin in quantum field theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of this formalism is that it enables us to study implications of the double copy in classical gravity. We discuss examples of observables including the total change of a particle's momentum, and the gravitational waveform, during a scattering encounter. The double copy also allows direct access to classical solutions in gravity. We review this classical double copy starting from its linearised level, where it originates in the double copy of three-point amplitudes. The classical double copy extends elegantly to exact solutions, making a connection between scattering amplitudes and the geometric formulation of General Relativity.