Gravitational shock waves and scattering amplitudes

TL;DR

This paper uses scattering amplitude techniques to analyze gravitational shock waves, providing new derivations, generalizations, and insights into their classical solutions, spin effects, and scattering properties.

Contribution

It introduces a novel amplitude-based derivation of gravitational shock waves and explores their relation to electromagnetic shock waves and spinning sources, including exact solutions and scattering predictions.

Findings

Derived gravitational shock waves from scattering amplitudes.

Established a classical double copy relating gravity and electromagnetism.

Computed scattering angles for spinning shock waves to all orders in spin.

Abstract

We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by exploiting a novel relation between scattering amplitudes and solutions to Einstein's field equations. We prove that gravitational shock waves arise from the classical part of a three point function with two massless scalars and a graviton. The region where radiation is localized has a distributional profile and it is now recovered in a natural way, thus bypassing the introduction of singular coordinate transformations as used in General Relativity. The computation is easily generalized to arbitrary dimensions and we show how the exactness of the classical solution follows from the absence of classical contributions at higher loops. A classical double copy between gravitational and electromagnetic shock waves is also provided and for a spinning source, using the exponential form of three point amplitudes, we infer a remarkable relation between gravitational shock waves and spinning ones, also known as gyratons. Using this property, we infer a family of exact solutions describing gravitational shock waves with spin. We then compute the phase shift of a particle in a background of shock waves finding agreement with an earlier computation by Amati, Ciafaloni and Veneziano for particles in the high energy limit. Applied to a gyraton, it provides a result for the scattering angle to all orders in spin.