Classical double copy of black strings in an Anti-de Sitter background

TL;DR

This work tests the classical double copy for curved, extended gravitational objects by casting static black strings in AdS into Kerr--Schild form over a cylindrical background. The authors construct the single-copy gauge fields and zeroth-copy scalars from the KS perturbation $\mathcal{H}(r)$, showing that neutral black strings yield a cylindrically electrostatic field sourced by an infinite line of color charge, while the charged case adds a distributed bulk current; in both cases the scalar copy satisfies a conformally coupled scalar equation on AdS. The results demonstrate a consistent gravity--gauge--scalar correspondence for extended objects in curved spacetime and illustrate how spacetime curvature itself can act as an effective source in the scalar sector. Potential future directions include rotating black strings and regular (black-bounce) string solutions, as well as applications to other curved backgrounds and higher dimensions.

Abstract

We study the classical double copy for static black string solutions in an Anti--de Sitter (AdS) background. By casting the black string metric into Kerr--Schild form over a cylindrical AdS geometry, we construct the corresponding single and zeroth copies. The single copy describes a gauge field satisfying Maxwell-like equations and sourced by an effective line of color charge, while the zeroth copy is given by a scalar field conformally coupled to the AdS background. We also extend the analysis to charged black strings, identifying the associated modifications in the gauge sector. These results show that the classical double copy consistently applies to extended gravitational objects in curved spacetimes.