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

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.