Color-Kinematics Duality and the Double Copy in Curved Spacetimes

Abstract

The double copy relates gravitational data to gauge-theory data, most sharply through color-kinematics duality for flat-space scattering amplitudes. This review surveys the extent to which this idea can be formulated beyond asymptotically flat backgrounds. After recalling the flat-space ingredients needed for comparison, we describe curved-space constructions for boundary correlators and scattering observables in AdS, dS, and other non-trivial backgrounds. We then review classical and field-level maps, including Kerr--Schild, Weyl, Cotton, twistor, and convolutional double copies. A separate part is devoted to self-dual sectors. Throughout, we emphasize both the common structures that survive from flat space and the obstructions introduced by curvature.