  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.
