String clouds and radiation flows as sources of gravity in static or rotating cylinders (1909.09409v1)

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.