A spinorial double copy for ${\cal N}=0$ supergravity

The Weyl double copy is a formula relating solutions of scalar, gauge and gravity theories, and is related to the BCJ double copy for scattering amplitudes. The latter relates Yang-Mills theory to ${\cal N}=0$ supergravity, where an axion and dilaton are present in addition to the graviton. However, the traditional Weyl double copy applies only to pure gravity solutions, such that it remains to be seen whether or not it can be extended to the full spectrum of ${\cal N}=0$ supergravity. We examine this question using recently developed twistor methods, showing that some sort of double copy formula for ${\cal N}=0$ supergravity is indeed possible for certain solutions. However, it differs both from the traditional Weyl double copy form, and recent conjectures aimed at generalising the Weyl double copy to non-vacuum solutions.