Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction

TL;DR

This work extends the Weyl double copy to slowly rotating black holes in dynamical Chern-Simons gravity by employing a perturbative slow-rotation expansion. It derives corrected electromagnetic fields for Petrov type D and type I spacetimes via two decomposition schemes, revealing CS-induced contributions to $F_{r\phi}$ and associated currents that often cancel in total, consistent with the underlying metric corrections. The results demonstrate the viability of a sourced Weyl double copy in CS gravity and clarify how spacetime algebraic type governs the presence of sources in Maxwell equations. Overall, the study links gravitational CS modifications to structured electromagnetic corrections through the double-copy framework, highlighting the interplay between metric deformations and gauge-field sources.

Abstract

The Weyl double copy builds the relation between gauge theory and gravity theory, especially the correspondence between gauge solutions and gravity solutions. In this paper, we obtain the slowly rotating charge solutions from Weyl double copy for the Kerr black hole with small Chern-Simons correction. Based on the Weyl double copy relation, for the Petrov type D solution, we find the additional correction to the electromagnetic field strength tensor of rotating charge. For the Petrov type I solution, we find that the additional electromagnetic field strength tensors have the exogenous properties, while the total sources vanish at the leading order.