The Classical Double Copy of a Point Charge

Abstract

The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically flat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory. The latter formalism exhibits the relation between the Kerr-Schild classical double copy and the string theory origin of the double copy for scattering amplitudes.

arXiv comment24 pages. v2: minor changes, published version

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• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• A Twistorial Foundation for the Classical Double Copy
• The Weyl Double Copy for Gravitational Waves
• Classical Solutions and their Double Copy in Split Signature
• Topology and Wilson lines: global aspects of the double copy
• The classical double copy of non-singular black holes
• Covariant Color-Kinematics Duality
• The convolutional double copy: a case study with a point
• A double copy for asymptotic symmetries in the self-dual sector
• Classical Yang-Mills observables from amplitudes
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Ehlers as EM duality in the double copy
• Weyl doubling
• The Newman-Penrose Map and the Classical Double Copy
• Monopoles, shockwaves and the classical double copy
• Strings, extended objects, and the classical double copy
• Double Field Theory as the Double Copy of Yang-Mills
• New heavenly double copies
• Massive Gravity from Double Copy
• Asymptotic Weyl Double Copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Einstein-Maxwell theory and the Weyl double copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Twistor Space Origins of the Newman-Penrose Map
• On the Lagrangian formulation of the double copy to cubic order
• Geodesics From Classical Double Copy
• Isometries and the double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
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• Classical Double Copy of Spinning Worldline Quantum Field Theory
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• Note on the asymptotic structure of Kerr-Schild form
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• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• New framework for classical double copies
• The Weyl double copy from twistor space
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• The Kerr-Schild Double Copy in Lifshitz Spacetime