The Radiative Double Copy for Einstein-Yang-Mills Theory

TL;DR

This paper demonstrates that a radiative double copy formalism connects Einstein-Yang-Mills solutions with Yang-Mills coupled to a biadjoint scalar, supporting the idea that gauge and gravity solutions are fundamentally related.

Contribution

It extends the double-copy formalism to Einstein-Yang-Mills theory, showing a correspondence at the lowest finite order.

Findings

Double copy relates Einstein-Yang-Mills to Yang-Mills with biadjoint scalar.

Trace-reversed metric is a natural double copy of gauge field.

Supports gauge-gravity solution correspondence despite different Lagrangians.

Abstract

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric $\bar{h}^{\mu\nu}$ is a natural double copy of the gauge boson $A^{\mu a}$. This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.