In this paper, we discuss general relativistic, self-gravitating and
uniformly rotating perfect fluid bodies with a toroidal topology (without
central object). For the equations of state describing the fluid matter we
consider polytropic as well as completely degenerate, perfect Fermi gas models.
We find that the corresponding configurations possess similar properties to the
homogeneous relativistic Dyson rings. On the one hand, there exists no limit to
the mass for a given maximal mass-density inside the body. On the other hand,
each model permits a quasistationary transition to the extreme Kerr black hole.Comment: 6 pages, 4 figures, added material and one new referenc
