The interior solution of axially symmetric, stationary and rigidly   rotating dust configurations
  It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations. 
Norman G\"urlebeck
gr-qc astro-ph.GA