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

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.

The SAGEX review on scattering amplitudes*

“…At the same time, this shows full agreement between the eikonal formalism and the formulation based on the exponential representation of the amplitude. [14] Scattering amplitudes capture basic on-shell physical information in a beautifully simple form. Although the amplitudes have their origin in quantum field theory, they have wide-ranging applications even in classical physics.…”

Einstein-Maxwell theory and the Weyl double copy

“…That is, since the PD metric is not asymptotically flat, the single copy gauge fields are sourced by both an electric and magnetic current density. 14…”

“…This result was anticipated by the Kawai-Lewellen-Tye (KLT) relation demonstrating any closed string amplitude may be cast as a linear sum of factors, each of which is a product of two open string amplitudes, at tree level [4]. The discovery of the double copy resulted in powerful new techniques for computing amplitudes in (super)gravity at tree-level and beyond [3,[5][6][7][8], offering new insights into the fundamental nature of perturbative quantum gravity, and has numerous applications, particularly in gravitational wave physics [9][10][11][12] (see [13][14][15] for comprehensive reviews).…”

Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order

“…Similarly, the post-Minkowskian (PM) approximation is a weak-field expansion, but places no restriction on the magnitude of velocities. Next to entirely classical approaches to the PM approximation [17][18][19][20][21][22][23][24][25], recent progress is pioneered by methods starting out from (quantum) scattering amplitudes [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. In addition, manifestly classical methods that make use of quantumfield-theory techniques show great promise for advancing the PM approximation, namely effective field theory [40][41][42][43][44][45] and worldline quantum field theory [46,47] approaches.…”