Quasi-stationary routes to the Kerr black hole

TL;DR

This paper explores the transition process from rotating fluid bodies to Kerr black holes, demonstrating that such a transition necessarily passes through the extreme Kerr solution, supported by analytical and numerical results.

Contribution

It provides a rigorous condition for the black hole limit of rotating fluid bodies and generalizes analytical results to numerical studies of rotating fluid rings.

Findings

Black hole limit occurs when gravitational mass equals twice the product of angular velocity and angular momentum.

Quasi-stationary routes to black holes pass through the extreme Kerr solution.

Analytical results for dust disks are extended to fluid rings with various equations of state.

Abstract

Quasi-stationary (i.e. parametric) transitions from rotating equilibrium configurations of fluid bodies to rotating black holes are discussed. For the idealized model of a rotating disc of dust, analytical results derived by means of the "inverse scattering method" are available. They are generalized by numerical results for rotating fluid rings with various equations of state. It can be shown rigorously that a black hole limit of a fluid body in equilibrium occurs if and only if the gravitational mass becomes equal to twice the product of angular velocity and angular momentum. Therefore, any quasi-stationary route from fluid bodies to black holes passes through the extreme Kerr solution.