Eikonal scattering in Kaluza-Klein gravity

We study eikonal scattering in the context of Kaluza-Klein theory by considering a massless scalar field coupled to Einstein’s gravity in 5D compactified to 4D on a manifold M4 × S1. We also examine various different kinematic limits of the resulting eikonal. In the ultra-relativistic scattering case we find correspondence with the time delay calculated for a massless particle moving in a compactified version of the Aichelburg-Sexl shock-wave geometry. In the case of a massless Kaluza-Klein scalar scattering off a heavy Kaluza-Klein mode a similar calculation yields the deflection angle of a massless particle in the geometry of an extremal, Q = 2M , Einstein-Maxwell-dilaton 4D black hole. We also discuss a related case in the scattering of dilatons off a large stack of D0-branes or D6-branes in dimensionally reduced D = 10 type IIA string theory.