Gravitational radiation from the classical spinning double copy

TL;DR

This work extends the BCJ classical double copy to radiative processes from spinning sources, establishing a precise correspondence between perturbative Yang–Mills radiation and gravitational radiation in a theory that includes the graviton, dilaton, and axion. Using spin as a dynamical degree of freedom on worldlines and applying color–kinematic substitutions, the authors derive the gravitational amplitudes from Yang–Mills data and fix the required spin couplings by Ward-identity constraints, including the essential condition $\kappa=-1$. They construct the bulk gravity action consistent with the double copy, fixing the axion interaction and the dilaton–axion couplings, and compute the axion, dilaton, and graviton radiation amplitudes to linear order in spin, showing exact agreement with the double-copy predictions. This nontrivial check strengthens the classical double copy as a practical tool for gravitational wave observables and highlights the role of additional fields (axion and dilaton) in the radiative sector, while outlining paths to obtain pure GR results at higher orders. The work points toward broader applicability to astrophysical sources and motivates further development to higher-spin and higher-order corrections, as well as strategies to suppress extra fields for direct GR comparisons.

Abstract

We establish a correspondence between perturbative classical gluon and gravitational radiation emitted by spinning sources, to linear order in spin. This is an extension of the non-spinning classical perturbative double copy and uses the same color-to-kinematic replacements. The gravitational theory has a scalar (dilaton) and a 2-form field (the Kalb-Ramon axion) in addition to the graviton. In arXiv:1712.09250, we computed axion radiation in the gravitational theory to show that the correspondence fixes its action. Here, we present complete details of the gravitational computation. In particular, we also calculate the graviton and dilaton amplitudes in this theory and find that they precisely match with the predictions of the double copy. This constitutes a non-trivial check of the classical double copy correspondence, and brings us closer to the goal of simplifying the calculation of gravitational wave observables for astrophysically relevant sources.

Figures (4)

• Figure 1: Feynman diagrams that contribute to leading order gluon radiation. Diagram $(a)$ corresponds to the spin-independent contribution to the source current $\tilde{J}^\mu_a(k)$. Diagrams $(b)$-$(d)$ correspond to spin-dependent contributions to the source current.
• Figure 2: Feynman diagrams for the perturbative expansion of the axion source current $\tilde{ J}^{\mu\nu}(k)$ up to $\mathcal{O}(\eta^2)$, with a single spin insertion. Here, wavy lines, curvy lines and dashed lines respectively represent gravitons, axions and dilatons. Diagrams $(a)-(b)$ represent axion radiation coming directly off the worldline. Diagrams $(c)-(d)$ correspond to axion radiation from bulk dilaton and graviton vertices.
• Figure 3: Feynman diagrams that contribute to the energy-momentum pseudotensor $\tilde{T}^{\mu\nu}(k)$ at $\mathcal{O}(\eta^2)$, with a single spin insertion. Diagram $(a)$ represents graviton radiation from corrections to the spin-independent piece due to the equations of motion. Diagrams $(b)-(d)$ correspond to corrections at linear order in spin.
• Figure 4: Feynman diagrams contributing to the dilaton source $\tilde{J}(k)$ at $\mathcal{O}(\eta^2)$, with a single spin insertion. As earlier, the dashed lines and the wavy lines represent the dilaton and the graviton respectively. Diagram $(a)$ represents corrections to the spin-independent piece of $\tilde{J}(k)$ due to the equations of motion. Diagrams $(b)-(c)$ correspond to a single spin insertion.