Deriving Weyl double copies with sources
Kymani Armstrong-Williams, Nathan Moynihan, Chris D. White
Abstract
A bstract The Weyl double copy is a relationship between classical solutions in gauge and gravity theories, and has previously been applied to vacuum solutions in both General Relativity and its generalisations. There have also been suggestions that the Weyl double copy should extend to solutions with non-trivial sources. In this paper, we provide a systematic derivation of sourced Weyl double copy formulae, using spinorial methods previously established for $$\mathcal{N}$$ = 0 supergravity. Our results apply at linearised level, but can be promoted to exact statements in special cases. As a cross-check, we rederive the same formulae using a tensorial approach, which then allows us to extend our arguments to sources containing arbitrary powers of the inverse radial coordinate. We also generalise our results to include the Kerr-Newman black hole, clarifying previous alternative double copy formulae presented in the literature. Our results extend the validity of the Weyl double copy, and may be useful for further astrophysical applications of this correspondence.