Do rotating dust stars exist in general relativity?

If rotating dust stars would exist in general relativity, they would represent examples of an improbable complete balance between the attractive quasi-Newtonian force (gravitoelectricity) and the repulsive gravitomagnetism. However, nonexistence proof is available hitherto only for some dust 'stars' extending to infinity and for isolated dust stars of a very restricted class. By analyzing the lines of constant generalized Newtonian potential U in the interior and exterior of a large class of (hypothetical) stationary and axisymmetrically rotating dust stars in general relativity, we find that the existence of such stars can be disproved as soon as minima of the potential U in the exterior vacuum region can be excluded. We present some ideas of how this minimum problem could be attacked, and we summarize the present knowledge about Newtonian and Einsteinian rotating dust systems.