Relativistically rotating dust cylinders

Abstract

A previously derived method for obtaining the general differentially rotating dust metric is applied to the cylindrically symmetric case. The dust metric, the exterior vacuum metric, the matching conditions at the boundary, and the asymptotic behavior at infinity are worked out explicitly. As a special case, the solutions include van Stockum's rigidly rotating models. Inertial dragging effects are found to be enhanced when the angular velocity decreases outward so that the angular momentum is concentrated near the axis. In the extreme relativistic case, the null cones emanating from points on the axis develop a caustic surface at which they turn around and eventually refocus at the axis. However, this is associated with acausal behavior rather than horizons.