Classical double copy at null infinity

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.

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

“…Still, there is hope that both approaches can be reconciled through the connection with amplitudes. For instance, amplitudes in self-dual gravity are known to be 1-loop exact [129], which suggests a close connection to the exact Penrose transform (see [69,80,130,131] for related recent works).…”

“…Let us give a pragmatical introduction to the basic ingredients of twistor theory, see [69,[78][79][80] for recent reviews. As it turns out, the theory is especially suitable for both (2,2) and (1,3) signatures.…”

“…The main geometrical tool of this note is twistor theory. Two complementary perspectives play a role: On the one hand, given that twistors beautifully parametrize null geodesics, they can be directly used to reconstruct purely radiative fields from their asymptotic data at future null infinity, through the Kirchoff-d'Adhémar formula [66][67][68][69]. This application emerges naturally for the (1, 3) S-Matrix.…”

NS-NS Spacetimes from Amplitudes

“…In this Weyl form, the classical double copy was applied to all vacuum Petrov type D solutions of the Einstein equation and has been explored also for vacuum type N solutions [125]. A twistorial interpretation of the Weyl double copy is being developed in [126][127][128][129][130][131][132].…”

Note on the asymptotic structure of Kerr-Schild form

“…Note added: When writing up this paper, we became aware of [40,41] with overlapping motivations with ours.…”