Equatorial circular motion in Kerr spacetime

TL;DR

This paper investigates the properties and stability of equatorial circular orbits around Kerr spacetime objects, revealing differences between black holes and naked singularities, including unique zero angular momentum orbits.

Contribution

It provides a comprehensive analysis of circular orbits in Kerr spacetime, identifying stability zones and zero angular momentum radii, highlighting differences between black holes and naked singularities.

Findings

Identified all radii with zero angular momentum orbits due to repulsive gravity.

Classified stability zones of circular orbits for black holes and naked singularities.

Showed that stability zone structures differ significantly between black holes and naked singularities.

Abstract

We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circular orbits. It is shown that the geometric structure of the stability zones of black holes is completely different from that of naked singularities.