Kerr-Schild Double Copy of the Randall-Sundrum Black String

TL;DR

This paper constructs the Kerr-Schild double copy for the Randall-Sundrum black string, deriving gauge and scalar fields and analyzing their equations in a warped extra dimension context.

Contribution

It provides the first explicit Kerr-Schild double copy construction for the Randall-Sundrum black string, including novel insights into the field equations and alternative splitting effects.

Findings

Single copy gauge field is sourceless and independent of the holographic coordinate.

Zeroth copy scalar obeys a modified Klein-Gordon equation with an effective mass.

Alternative splitting yields a physically inequivalent double copy with delocalized bulk current.

Abstract

We construct the Kerr-Schild classical double copy of the black string in the Randall-Sundrum II model, deriving the single and zeroth copies, and verifying the associated field equations. The single copy gauge field is independent of the holographic coordinate and satisfies a sourceless Maxwell equation on the curved background, in direct analogy with the Coulomb field of the Schwarzschild double copy. The zeroth copy scalar obeys a modified Klein-Gordon equation with a first-order derivative term along the extra dimension; a field redefinition yields a standard Klein-Gordon equation with effective mass $m^2 = 12/l^2$, induced by the warp factor. We further show that an alternative Kerr-Schild splitting, gravitationally equivalent to the canonical one, produces a physically inequivalent double copy: the gauge field is supported by a conserved but delocalized bulk current, and the zeroth copy satisfies a massless equation that carries no imprint of the warped extra dimension.