Geodesic structure of five-dimensional non-asymptotically flat 2-branes

TL;DR

This paper analyzes the geodesic structure of a five-dimensional dilatonic 2-brane with non-asymptotic flatness, revealing unique causal regions and contrasting energy behaviors of null and timelike geodesics.

Contribution

It provides a detailed study of geodesics in a non-asymptotically flat 2-brane spacetime, highlighting the effects of naked singularities and the warp function's divergence.

Findings

Identifies two causally disconnected regions due to singularities.

Shows opposing energy requirements for null and timelike geodesics.

Analyzes the impact of the warp function's divergence on geodesic behavior.

Abstract

We study the geodesics of a five dimensional non-asymptotically flat dilatonic 2-brane. Although the metric's warp function diverges logarithmically in the far field region of the transverse space, the curvature does not. The brane has two naked singularities, the usual central singularity and a circular singularity at the radius where the warp function vanishes. This creates two causally disconnected regions of the transverse space. Using the methods of energy conservation and effective potentials we study the null and timelike orbital and radial geodesics in both regions and show that they exhibit opposing energy requirements.