  The double copy relates scattering amplitudes in gauge and gravity theories.
In this paper, we expand the scope of the double copy to construct spacetime
metrics through a systematic perturbative expansion. The perturbative procedure
is based on direct calculation in Yang-Mills theory, followed by squaring the
numerator of certain perturbative diagrams as specified by the double-copy
algorithm. The simplest spherically symmetric, stationary spacetime from the
point of view of this procedure is a particular member of the
Janis-Newman-Winicour family of naked singularities. Our work paves the way for
applications of the double copy to physically interesting problems such as
perturbative black-hole scattering.
