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.

44 pages, 2 figures. v2: additions to references and discussion

References in corpus (28)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• New symmetries for the Gravitational S-matrix
• Scattering on plane waves and the double copy
• A Twistorial Foundation for the Classical Double Copy
• Perturbative gravity at null infinity
• Ambitwistor strings at null infinity and subleading soft limits
• The Weyl Double Copy for Gravitational Waves
• Classical Solutions and their Double Copy in Split Signature
• Shifting Spin on the Celestial Sphere
• A double copy for asymptotic symmetries in the self-dual sector
• Perturbative gauge theory at null infinity
• The Newman-Penrose Map and the Classical Double Copy
• Celestial double copy from the worldsheet
• New heavenly double copies
• Asymptotic Weyl Double Copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• Twistor Space Origins of the Newman-Penrose Map
• The double copy of the multipole expansion
• Geodesics From Classical Double Copy
• Gluon scattering on self-dual radiative gauge fields
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Yang-Mills Theory in Twistor Space
• The conformal Einstein field equations and the local extension of future null infinity
• Amplitudes from Coulomb to Kerr-Taub-NUT
• Dual Komar Mass, Torsion and Riemann-Cartan Manifolds
• Subleading BMS Charges and The Lorentz Group

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• Off-Shell Color-Kinematics Duality for Chern-Simons
• Celestial chiral algebras, colour-kinematics duality and integrability
• Asymptotic Weyl Double Copy
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Einstein-Maxwell theory and the Weyl double copy
• Alternative formulations of the twistor double copy
• The double copy of the multipole expansion
• Graviton scattering in self-dual radiative space-times
• Why is the Weyl double copy local in position space?
• Non-perturbative aspects of the self-dual double copy
• Isometries and the double copy
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Weyl double copy and massless free fields in curved spacetimes
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Planar solutions of higher-spin theory. Nonlinear corrections
• Regularized Weyl double copy
• Note on the asymptotic structure of Kerr-Schild form
• Classical double copy and higher-spin fields
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Asymptotic Weyl double copy in Newman-Penrose formalism
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Weyl double copy in type D spacetime in four and five dimensions
• Hawking radiation from the double copy
• New framework for classical double copies
• Asymptotic symmetries and memories of gauge theories in FLRW spacetimes
• Five dimensional Weyl double copy
• The Radial Action from Probe Amplitudes to All Orders
• NS-NS Spacetimes from Amplitudes
• Weyl double copy in Lifshitz spacetimes