The Classical Double Copy of a Point Charge

TL;DR

This paper develops two formalisms for relating the Coulomb solution in gauge theory to a class of gravity solutions, extending the classical double copy concept through perturbative and exact methods, including a novel Kerr-Schild approach.

Contribution

It introduces a perturbative and an exact double copy formalism for static solutions, including a new Kerr-Schild generalization inspired by double field theory.

Findings

Established a perturbative double copy for Coulomb and Janis-Newman-Winicour solutions.

Presented an exact double copy map with a novel Kerr-Schild formalism.

Linked the classical double copy to string theory origins.

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.