Bound states and the classical double copy

TL;DR

This paper extends the classical double copy framework to bound systems, enabling the mapping of gluon radiation in gauge theory to gravitational radiation in dilaton gravity, with applications to post-Newtonian systems.

Contribution

It generalizes the classical double copy to bound systems and derives gravitational radiation fields from gauge theory in generic orbits.

Findings

Mapped gluon emission to dilaton gravity radiation fields.

Reproduced post-Newtonian gravitational radiation from gauge theory.

Validated the double copy approach for bound systems.

Abstract

We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits. As an application, we reproduce the leading post-Newtonian radiation fields and energy flux for point masses in non-relativistic orbits from the double copy of gauge theory.