Uniformly Rotating Rings in General Relativity

TL;DR

This paper explores self-gravitating, uniformly rotating fluid rings in general relativity, analyzing their properties with different equations of state and their potential to transition into extreme Kerr black holes.

Contribution

It provides a detailed study of relativistic rotating rings with various matter models, highlighting their properties and connection to black hole limits.

Findings

No mass limit for given maximal density

Configurations can transition to extreme Kerr black holes

Similar properties to homogeneous relativistic Dyson rings

Abstract

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.