TL;DR
This paper presents a family of cylindrical solutions to Einstein's equations involving Bessel functions, including regular matter cylinders like the Gott-Hiscock string, with implications for mass limits and dynamic behaviors.
Contribution
It introduces new cylindrical solutions with Bessel function metrics, expanding the set of known Einstein solutions for power law densities.
Findings
Solutions include the Gott-Hiscock string and Airy function cylinders.
All solutions adhere to the Vilenkin mass per length limit.
Examples of Bessel shells and motion are provided.
Abstract
A set of cylindrical solutions to Einstein's field equations for power law densities is described. The solutions have a Bessel function contribution to the metric. For matter cylinders regular on axis, the first two solutions are the constant density Gott-Hiscock string and a cylinder with a metric Airy function. All members of this family have the Vilenkin limit to their mass per length. Some examples of Bessel shells and Bessel motion are given.
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