Spacetime structure of 5D hypercylindrical vacuum solutions with tension

TL;DR

This paper explores the geometric properties of five-dimensional cylindrical vacuum solutions with tension, classifying them by tension-to-mass ratio and analyzing their singularity structures, including black strings and naked singularities.

Contribution

It provides a classification of 5D cylindrical vacuum solutions based on tension-to-mass ratio and examines their geometric and singularity features.

Findings

Schwarzschild black string has a horizon enclosing a curvature singularity.

Solutions with naked singularities exhibit finite emission time but infinite redshift.

Geometric properties depend on the tension-to-mass ratio of the solutions.

Abstract

We investigate geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and 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 geometry of other solutions which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer with finite time, but is infinitely red-shifted.