Nonrigidly rotating stationary cylindrical dust spacetimes

In this paper, we consider stationary rotating cylindrically symmetric dust spacetimes. We first show that the Maitra spacetime is the unique nonrigidly (nonnull shear scalar) rotating solution with a regular axis and that is the most general one of the field equations. We are also able to demonstrate what Maitra’s paper does not show, where the solution is merely stated without any demonstration. Then we find that the nonrigidly rotating spacetimes, not necessarily regular, can be matched, across timelike cylindrical hypersurfaces, to a one-parameter family of stationary vacuum exteriors given by the Weyl class but not to the Lewis class, generalizing a result by Bonnor and Steidman. Among other properties, it is shown that the amount of rotating dust packed inside a cylinder is bigger if it is rigidly rotating than nonrigidly rotating. Finally, we show that in the nonrigidly rotating cases the fluid necessarily has vorticity and the spacetimes are not silent, where the magnetic part of the Weyl tensor is nonzero.