String clouds and radiation flows as sources of gravity in static or rotating cylinders

TL;DR

This paper explores exact solutions in general relativity for cylindrically symmetric spacetimes supported by cosmic strings and radiation flows, highlighting the existence, limitations, and physical implications of these configurations.

Contribution

It provides new exact solutions for static and stationary cylindrically symmetric spacetimes with cosmic strings and radiation flows, analyzing their properties and physical viability.

Findings

Static solutions with z- and φ-directed radiation flows do not exist.

Solutions with z-directed strings require negative energy density.

Most solutions contain singularities and regions with closed timelike curves.

Abstract

Static and stationary cylindrically symmetric space-times in general relativity are considered, supported by distributions of cosmic strings stretched in the azimuthal ($\varphi$), longitudinal ($z$) or radial ($x$) directions or and by pairs of mutually opposite radiation flows in any of these directions. For such systems, exact solutions are obtained and briefly discussed, except for radial strings (a stationary solution for them is not found); it is shown that static solutions with $z$- and $\varphi$-directed radiation flows do not exist, while for $z$-directed strings a solution is only possible with negative energy density. Almost all solutions under discussion contain singularities, and all stationary solutions have regions with closed timelike curves, hence only their well-behaved regions admit application to real physical situations.