The double copy: Bremsstrahlung and accelerating black holes

TL;DR

This paper explores the classical double copy correspondence between gravity and gauge theory for accelerating, radiating sources, extending previous stationary solutions to dynamic cases and linking it to scattering amplitudes.

Contribution

It demonstrates the double copy for a time-dependent, radiating gravitational solution with a non-trivial stress-energy tensor, connecting it to the BCJ double copy for scattering amplitudes.

Findings

Established the double copy for accelerating, radiating sources.

Linked classical solutions to gauge theoretic currents.

Provided scattering amplitude calculations consistent with the double copy.

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.