How small can an over-spinning body be in general relativity?

TL;DR

This paper explores the limits of how small an over-spinning body can be in general relativity, examining conditions under which naked singularities might form or be transient, and implications for cosmic censorship.

Contribution

It provides a kinematical estimate and initial data analysis showing that over-spinning bodies can transiently resemble Kerr naked singularities, challenging assumptions about their minimum size.

Findings

Over-spinning bodies can produce near-Kerr naked singularity geometries transiently.

A minimum size for over-spinning bodies is suggested by particle approach estimates.

Naked singularity-like geometries may appear temporarily without collapsing into singularities.

Abstract

The angular momentum of the Kerr singularity should not be larger than a threshold value so that it is enclosed by an event horizon: The Kerr singularity with the angular momentum exceeding the threshold value is naked. This fact suggests that if the cosmic censorship exists in our Universe, an over-spinning body without releasing its angular momentum cannot collapse to spacetime singularities. A simple kinematical estimate of two particles approaching each other supports this expectation and suggests the existence of a minimum size of an over-spinning body. But this does not imply that the geometry near the naked singularity cannot appear. By analyzing initial data, i.e., a snapshot of a spinning body, we see that an over-spinning body may produce a geometry close to the Kerr naked singularity around itself at least as a transient configuration.