  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 $M_4\times S^1 $. 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.
