The ergoregion in the Kerr spacetime: properties of the equatorial circular motion

TL;DR

This paper thoroughly examines the properties of equatorial circular motion within the ergoregion of Kerr spacetime, revealing features that distinguish black holes from naked singularities and implications for astrophysical observations.

Contribution

It provides a detailed analysis of stability, energy, and angular momentum of particles, introducing a classification of Kerr spacetimes based on orbital motion properties.

Findings

Distinct stability regions differentiate black holes from naked singularities.

Presence of counterrotating and zero angular momentum particles indicates a repulsive gravitational field.

Orbital motion properties can classify Kerr spacetimes with astrophysical relevance.

Abstract

We investigate in detail the circular motion of test particles on the equatorial plane of the ergoregion in the Kerr spacetime. We consider all the regions where circular motion is allowed, and we analyze the stability properties and the energy and angular momentum of the test particles. We show that the structure of the stability regions has definite features that make it possible to distinguish between black holes and naked singularities. The naked singularity case presents a very structured non-connected set of regions of orbital stability, where the presence of counterrotating particles and zero angular momentum particles for a specific class of naked singularities is interpreted as due to the presence of a repulsive field generated by the central source of gravity. In particular, we analyze the effects of the dynamical structure of the ergoregion (the union of the orbital regions for different attractor spins) on the behavior of accretion disks around the central source. The properties of the circular motion turn out to be so distinctive that they allow the introduction of a complete classification of Kerr spacetimes, each class of which is characterized by different physical effects that could be of especial relevance in observational Astrophysics. We also identify some special black hole spacetimes where these effects could be relevant.