# Eikonal Scattering in Kaluza-Klein Gravity

## TL;DR

This paper investigates eikonal scattering in Kaluza-Klein gravity, revealing connections with shock-wave geometries and black hole deflections, and extends the analysis to string theory brane configurations.

## Contribution

It provides a detailed analysis of eikonal scattering in Kaluza-Klein theory, linking scattering results to known geometries and black hole solutions, and explores related string theory scenarios.

## Key findings

- Eikonal scattering matches time delay in compactified shock-wave geometry.
- Deflection angles correspond to extremal Einstein-Maxwell-dilaton black holes.
- Analysis extends to dilaton scattering off D-branes in string theory.

## Abstract

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.