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We study an exact solution of Einstein's equations describing aself-gravitating system, made of dust, distributed with axial symmetry and instationary rotation, and we prove that this type of system has no Newtoniananalogue. In a low-energy limit, its existence depends on the solution of aGrad-Shafranov equation in vacuum which can be interpreted as a Laplaceequation for the toroidal component of the gravitomagnetic potential; inparticular, in this system the relativistic rotational effects are of the orderof magnitude of Newtonian ones. We therefore argue that this exact solutionshould contain singularities and discuss the possible consequences of usingsuch a system as simplified models for galactic dynamics.

Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects