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

Abstract

The Weyl double copy builds the relation between gauge theory and gravity theory, in particular the correspondence between gauge solutions and gravity solutions. In this paper, we obtain the slowly rotating charge solutions from the 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 in Chern–Simons modified gravity, we find the additional correction to the electromagnetic field strength tensor of the rotating charge. For the Petrov type I solution, we find that the additional electromagnetic field strength tensors have external sources, while the total sources vanish at the leading order.