Classical double copy at null infinity

TL;DR

This paper introduces two methods to construct gravitational solutions from gauge fields at null infinity, extending the classical double copy concept to asymptotically flat spacetimes and their radiative data.

Contribution

It presents novel prescriptions for the double copy at null infinity, applicable to radiative and asymptotic fields, linking gauge theory and gravity solutions in a new geometric context.

Findings

Constructed gravitational characteristic data from gauge fields via squaring

Extended double copy to asymptotic equations of motion and charges

Connected classical double copy with soft and hard sectors in scattering

Abstract

We give two double copy prescriptions which construct asymptotically flat solutions in gravity from asymptotically flat gauge fields. The first prescription applies to radiative fields, which are non-linear vacuum solutions determined by characteristic data at null infinity. For any two such radiative gauge fields (linear or non-linear), the characteristic data of a radiative metric, dilaton and axion is constructed by a simple `squaring' procedure, giving a classical double copy at the level of radiation fields. We demonstrate the procedure with several examples where the characteristic data can be explicitly integrated; for linear fields this also sheds light on the twistorial description of Weyl double copy. Our second prescription applies to all asymptotically flat fields at the level of their asymptotic equations of motion: we give a map between any solution of the asymptotic Maxwell equations and any solution of the asymptotic Einstein equations at null infinity. This also extends to the asymptotic charges and their duals, preserves the soft and hard sectors between gauge theory and gravity, and is related to the usual notion of double copy in scattering amplitudes.