Deriving Weyl double copies with sources

TL;DR

This paper systematically derives sourced Weyl double copy formulas using spinorial and tensorial methods, extending their applicability to solutions with sources and including the Kerr-Newman black hole, with potential astrophysical implications.

Contribution

It provides the first systematic derivation of sourced Weyl double copy formulas and extends their validity to solutions with arbitrary source structures and the Kerr-Newman black hole.

Findings

Derived sourced Weyl double copy formulas using spinorial methods.

Extended the formulas to sources with inverse radial powers.

Included the Kerr-Newman black hole in the double copy framework.

Abstract

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 ${\cal N}=0$ supergravity. 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.