Double copy of the multipole expansion

Abstract

The classical double copy relates solutions of biadjoint, gauge, and gravity theories. The ultimate origin and scope of this correspondence remains mysterious, such that it is important to build a clear physical intuition of how the double copy operates. To this end, we consider the multipole expansion of exact classical solutions. Using a recently developed twistor translation of the classical double copy, we use well-established techniques to show that the multipole moments of arbitrary vacuum type-D gravity fields are exactly related to their counterparts in gauge and biadjoint scalar theories by the single and zeroth copies. We cross-check our results using previously obtained results for the Kerr metric and also provide new results for the ``square root'' of the Kerr-Taub-NUT solution.