Spacetime structure of 5D hypercylindrical vacuum solutions with tension

We investigate the geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and is characterized by tension and mass densities. The solutions are classified by the tension-to-mass ratio. One particular example is the well-known Schwarzschild black string, which has a curvature singularity enclosed by a horizon. We focus mainly on the geometries of the other solutions, which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer in finite time, but is infinitely red-shifted.