Abstract
Advances in our understanding of perturbation theory suggest the existence of a correspondence between classical general relativity and Yang-Mills theory. A concrete example of this correspondence, which is known as the double copy, was recently introduced for the case of stationary Kerr-Schild spacetimes. Building on this foundation, we examine the simple time-dependent case of an accelerating, radiating point source. The gravitational solution, which generalises the Schwarzschild solution, includes a non-trivial stress-energy tensor. This stress-energy tensor corresponds to a gauge theoretic current in the double copy. We interpret both of these sources as representing the radiative part of the field. Furthermore, in the simple example of Bremsstrahlung, we determine a scattering amplitude describing the radiation, maintaining the double copy throughout. Our results provide the strongest evidence yet that the classical double copy is directly related to the BCJ double copy for scattering amplitudes.
Highlights
Gauge theory counterparts at the level of diagrams
Our results provide the strongest evidence yet that the classical double copy is directly related to the BCJ double copy for scattering amplitudes
The BCJ prescription is to replace the colour factor of each diagram by an additional copy of the diagram’s kinematic numerator. This replacement must be performed in a particular representation of the amplitude, where the kinematic numerators satisfy the algebraic properties of the corresponding colour factor
Summary
Let us begin with a brief review of the Kerr-Schild double copy, originally proposed in [55, 56]. Yang-Mills amplitudes only obey the double copy when written in BCJ dual form, meaning that certain Jacobi relations are satisfied by the kinematic numerator functions [3,4,5]. It is not known what the analogue of this property is in the classical double copy procedure. All of these considerations suggest that the Kerr-Schild story forms part of a larger picture, and in order to explore this it is instructive to seek well-defined generalisations of the results of refs. All of these considerations suggest that the Kerr-Schild story forms part of a larger picture, and in order to explore this it is instructive to seek well-defined generalisations of the results of refs. [55, 56]
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