892 research outputs found
Disclosing connections between black holes and naked singularities: Horizon remnants, Killing throats and bottlenecks
We study the properties of black holes and naked singularities by considering
stationary observers and light surfaces in Kerr spacetimes. We reconsider the
notion of Killing horizons from a special perspective by exploring the entire
family of Kerr metrics. To this end, we introduce the concepts of extended
plane, Killing throats and bottlenecks for weak (slowly spinning) naked
singularities. Killing bottlenecks (or horizon remnants in analogy with the
corresponding definition of throats in black holes) are restrictions of the
Killing throats appearing in special classes of slowly spinning naked
singularities. Killing bottlenecks appear in association with the concept of
pre-horizon regime introduced in [1, 2]. In the extended plane of the Kerr
spacetime, we introduce particular sets, metric bundles, of metric tensors
which allow us to reinterpret the concept of horizon and to find connections
between black holes and naked singularities throughout the horizons. To
evaluate the effects of frame-dragging on the formation and structure of
Killing bottlenecks and horizons in the extended plane, we consider also the
Kerr-Newman and the Reissner-Norstrom spacetimes. We argue that these results
might be significant for the comprehension of processes that lead to the
formation and eventually destruction of Killing horizons.Comment: 33 pages, 32 multi-panels figures, 3 Table
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
Motion of charged test particles in Reissner--Nordstr\"om spacetime
We investigate the circular motion of charged test particles in the
gravitational field of a charged mass described by the Reissner-Nordstr\"om
(RN) spacetime. We study in detail all the spatial regions where circular
motion is allowed around either black holes or naked singularities. The effects
of repulsive gravity are discussed by finding all the circles at which a
particle can have vanishing angular momentum. We show that the geometric
structure of stable accretion disks, made of only test particles moving along
circular orbits around the central body, allows us to clearly distinguish
between black holes and naked singularities.Comment: 58 pages, 41 figures. To be published in Phys. Rev. D. This work
follows the paper "Circular motion of neutral test particles in
Reissner-Nordstr\'om spacetime" published in Phys.\ Rev.\ D \ Vol.83, No.2
with DOI: 10.1103/PhysRevD.83.024021 (arXiv:1012.5411v1 [astro-ph.HE]
Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization
We introduce normal coordinates on the infinite dimensional group
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on . For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
-primitiveness, which is shown to be equivalent to the one already in the
literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
Extracting information on black hole horizons
We present some features of Kerr black hole horizons that are replicated on
orbits accessible to outside observers. We use the concepts of horizon
confinement and replicas to show that outside the outer horizon there exist
photon orbits whose frequencies contain information about the inner horizon and
that can, in principle, be detected through the emission spectra of black
holes. It is shown that such photon orbits exist close to the rotation axis of
the Kerr geometry. We argue that these results could be used to recognize and
further investigate black holes and their horizonsComment: 7 pages; 2 multipanels figure
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