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

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.Comment: 19 pages, 9 figure multi-panels; 3 Tables. This and a slightly modified version with the addition of new references and some new discussion. To appear in EPJ

Observers in Kerr spacetimes: the ergoregion on the equatorial plane

We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between "weak" and "strong" singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak singularities as resulting from the spin variation of black holes. We also explore the main properties of zero angular momentum observers for different classes of black hole and naked singularity spacetimes.Comment: 20 pages, 13 multi-panels figures, 2 table

Vacuum initial data, singularities, and cosmic censorship

The formation of a naked singularity in a vacuum, asymptotically flat spacetime would be a clear violation of cosmic censorship. We find initial value solutions to Einstein's field equations that may lead to this behavior. We construct two families of asymptotically flat, axisymmetric vaccum solutions at a moment of time symmetry. The limiting members of these families are singular. Our first family represents a linear string of Schwarzschild black holes. We study the divergence of the gravitational tidal field outside the holes as their number along the string is increased. Our second family consists of prolate Brill gravitational wave packets. We examine the tidal field strength as the characteristic width of the wave is reduced towards zero. In both cases we find that configurations can be constructed with arbitrarily large fields that are not clothed by apparent horizons. These configurations are characterized by long, prolate concentrations of mass energy. We analyze our results in the context of the hoop conjecture