The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar

Understand

We formulate a version of the double copy for classical fields in curved spacetimes.

• We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space.
• At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution.
• Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions.