The rigidly rotating disk of dust and its black hole limit

TL;DR

This paper discusses an exact solution for a rotating disk of dust in general relativity, revealing a mass limit and a transition to a black hole, confirming long-standing conjectures.

Contribution

It provides the first exact global solution for a rotating dust disk in Einstein's theory, demonstrating the mass limit and black hole transition.

Findings

Existence of an upper mass limit for the disk at fixed angular momentum.

Transition from the disk solution to a Kerr black hole at the mass limit.

Confirmation of long-standing conjectures by Bardeen and Wagoner.

Abstract

The exact global solution of the Einstein equations [Neugebauer & Meinel, Phys. Rev. Lett. 75 (1995) 3046] describing a rigidly rotating, self-gravitating disk is discussed. The underlying matter model is a perfect fluid in the limit of vanishing pressure. The solution represents the general-relativistic analogue of the classical Maclaurin disk. It was derived by applying solution techniques from soliton theory to the axisymmetric, stationary vacuum Einstein equations. In contrast to the Newtonian solution, there exists an upper limit for the total mass of the disk - if the angular momentum is fixed. At this limit, a transition to a rotating black hole, i.e., to the Kerr solution occurs. Another limiting procedure leads to an interesting cosmological solution. These results prove conjectures formulated by Bardeen and Wagoner more than twenty-five years ago.