Hollow cosmic string: the general-relativistic hollow cylinder

TL;DR

This paper explores various spacetime geometries inside an infinite rotating hollow cylinder, revealing solutions like black holes, wormholes, and potential spontaneous compactification, expanding understanding of cosmic string models in general relativity.

Contribution

It provides a comprehensive analysis of possible interior metrics for rotating hollow cylinders, including novel solutions such as wormholes and compactification scenarios.

Findings

Existence of black-hole solutions within the cylinder

Presence of wormhole solutions under certain parameters

Potential spontaneous compactification to a torus

Abstract

We determine the different possible space-time metrics inside an infinite rotating hollow cylinder with given energy density and longitudinal and azimuthal stresses, the metric outside the cylinder being chosen of the spinning cosmic string type. The solutions we obtain for various domains of values of the cylinder parameters include a space-time with topologically Euclidean spatial sections, a black-hole solution, a quasi-regular solution, and various wormhole solutions. A solution which is regular only if the longitudinal dimension is compactified might approximately describe spontaneous compactification of the cylinder to a torus.