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.

24 pages. v2: minor changes, published version

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Cited by in corpus (5)

• A Twistorial Foundation for the Classical Double Copy
• Strings, extended objects, and the classical double copy
• On the Lagrangian formulation of the double copy to cubic order
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation