Relativistic Dyson Rings and Their Black Hole Limit

TL;DR

This paper explores the properties of rotating relativistic fluid bodies with toroidal shapes, demonstrating their transition to black holes and analyzing the limits of their mass and size.

Contribution

It introduces a numerical method to solve the field equations for relativistic Dyson rings and characterizes their transition to black holes.

Findings

Toroidal bodies can transition to extreme Kerr black holes.

Configurations at the mass-shedding limit are highly relativistic.

No apparent bound on gravitational mass near the black-hole limit.

Abstract

In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.