Relativistic Bessel cylinders

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.