The double copy: Bremsstrahlung and accelerating black holes

TL;DR

The paper extends the classical Kerr-Schild double copy to time-dependent, radiating systems by analyzing an accelerating point particle. It derives a KS gravity solution with a radiative stress-energy and a corresponding gauge theory single copy current, then shows that Fourier-space radiative sources yield Bremsstrahlung amplitudes in both theories that maintain the double copy structure. This provides strong evidence that the classical double copy is intimately connected to the BCJ double copy for scattering amplitudes, even in dynamical, radiative settings. The work also discusses energy-condition subtleties and outlines avenues for extending the framework beyond stationary KS solutions and Minkowski backgrounds.

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.

Figures (2)

• Figure 1: Geometric interpretation of the Kerr-Schild solution for an accelerated particle.
• Figure 2: Physical interpretation of $(k\cdot \dot{\lambda})$, where this denotes the component of acceleration in the direction $n^\mu$.