The rigidly rotating relativistic dust cylinder

The solution of van Stockum (1937) consists of a rotating dust interior, and three exterior metrics referring to different ranges of the mass per unit length. It has been stated in the literature that the exterior in static, but it is proved here that this is so only in the low-mass case. An examination of the Riemann tensor shows that van Stockum's spacetime is free from singularities and matter at radial infinity below a certain value of the mass per unit length. The ultrarelativistic case which has closed timelike lines, can occur at physically possible densities and radii.