Uniformly Rotating Rings in General Relativity

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 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 quasi-stationary transition to the extreme Kerr black hole