5,569 research outputs found
Strains and Jets in Black Hole Fields
We study the behaviour of an initially spherical bunch of particles emitted
along trajectories parallel to the symmetry axis of a Kerr black hole. We show
that, under suitable conditions, curvature and inertial strains compete to
generate jet-like structures.Comment: To appear in the Proceedings of the Spanish Relativity Meeting 2007
held in Tenerife (Spain) 3 Figure
Spinning test particles and clock effect in Kerr spacetime
We study the motion of spinning test particles in Kerr spacetime using the
Mathisson-Papapetrou equations; we impose different supplementary conditions
among the well known Corinaldesi-Papapetrou, Pirani and Tulczyjew's and analyze
their physical implications in order to decide which is the most natural to
use. We find that if the particle's center of mass world line, namely the one
chosen for the multipole reduction, is a spatially circular orbit (sustained by
the tidal forces due to the spin) then the generalized momentum of the test
particle is also tangent to a spatially circular orbit intersecting the center
of mass line at a point. There exists one such orbit for each point of the
center of mass line where they intersect; although fictitious, these orbits are
essential to define the properties of the spinning particle along its physical
motion. In the small spin limit, the particle's orbit is almost a geodesic and
the difference of its angular velocity with respect to the geodesic value can
be of arbitrary sign, corresponding to the spin-up and spin-down possible
alignment along the z-axis. We also find that the choice of the supplementary
conditions leads to clock effects of substantially different magnitude. In
fact, for co-rotating and counter-rotating particles having the same spin
magnitude and orientation, the gravitomagnetic clock effect induced by the
background metric can be magnified or inhibited and even suppressed by the
contribution of the individual particle's spin. Quite surprisingly this
contribution can be itself made vanishing leading to a clock effect
undistiguishable from that of non spinning particles. The results of our
analysis can be observationally tested.Comment: IOP macros, eps figures n. 12, to appear on Classical and Quantum
Gravity, 200
Kerr metric, static observers and Fermi coordinates
The coordinate transformation which maps the Kerr metric written in standard
Boyer-Lindquist coordinates to its corresponding form adapted to the natural
local coordinates of an observer at rest at a fixed position in the equatorial
plane, i.e., Fermi coordinates for the neighborhood of a static observer world
line, is derived and discussed in a way which extends to any uniformly
circularly orbiting observer there.Comment: 15 page latex iopart class documen
On gravitomagnetic precession around black holes
We compute exactly the Lense-Thirring precession frequency for point masses
in the Kerr metric, for arbitrary black hole mass and specific angular
momentum. We show that this frequency, for point masses at or close to the
innermost stable orbit, and for holes with moderate to extreme rotation, is
less than, but comparable to the rotation frequency. Thus, if the quasi
periodic oscillations (QPOs) observed in the modulation of the X-ray flux from
some black holes candidates are due to Lense-Thirring precession of orbiting
material, we predict that a separate, distinct QPO ought to be observed in each
object.Comment: Accepted for publication in MNRAS. MN-Latex, 2 figure
Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues
The Erlangian approximation of Markovian fluid queues leads to the problem of
computing the matrix exponential of a subgenerator having a block-triangular,
block-Toeplitz structure. To this end, we propose some algorithms which exploit
the Toeplitz structure and the properties of generators. Such algorithms allow
to compute the exponential of very large matrices, which would otherwise be
untreatable with standard methods. We also prove interesting decay properties
of the exponential of a generator having a block-triangular, block-Toeplitz
structure
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200
Scattering of spinning bodies by a radiation field in Schwarzschild spacetime
We extend the analysis of Poynting-Robertson effect, i.e., the deviation from geodesic motion of test particles due to scattering by a superposed radiation field to the Schwarzschild background, to the case of spinning bodies. The extra contribution of the deviation due to spin can be relevant for astrophysical systems like the binary pulsar system PSR J0737-3039 orbiting Sgr A∗, but not for the Earth-Sun system
Spacetime Slices and Surfaces of Revolution
Under certain conditions, a -dimensional slice of a
spherically symmetric black hole spacetime can be equivariantly embedded in
-dimensional Minkowski space. The embedding depends on a real parameter
that corresponds physically to the surface gravity of the black hole
horizon.
Under conditions that turn out to be closely related, a real surface that
possesses rotational symmetry can be equivariantly embedded in 3-dimensional
Euclidean space. The embedding does not obviously depend on a parameter.
However, the Gaussian curvature is given by a simple formula: If the metric is
written , then
\K_g=-{1/2}\phi''(r).
This note shows that metrics and occur in dual pairs, and that
the embeddings described above are orthogonal facets of a single phenomenon. In
particular, the metrics and their respective embeddings differ by a Wick
rotation that preserves the ambient symmetry.
Consequently, the embedding of depends on a real parameter. The ambient
space is not smooth, and is inversely proportional to the cone angle
at the axis of rotation. Further, the Gaussian curvature of is given
by a simple formula that seems not to be widely known.Comment: 15 pages, added reference
Dark energy from cosmological fluids obeying a Shan-Chen nonideal equation of state
We consider a Friedmann-Robertson-Walker universe with a fluid source obeying a nonideal equation of state with ‘‘asymptotic freedom,’’ namely ideal gas behavior (pressure changes directly proportional to density changes) both at low and high density regimes, following a fluid dynamical model due to Shan and Chen. It is shown that, starting from an ordinary energy density component, such fluids naturally evolve towards a universe with a substantial ‘‘dark energy’’ component at the present time, with no need of invoking any cosmological constant. Moreover, we introduce a quantitative indicator of darkness abundance, which provides a consistent picture of the actual matter-energy content of the Universe
Electrocardiogram of the Mixmaster Universe
The Mixmaster dynamics is revisited in a new light as revealing a series of
transitions in the complex scale invariant scalar invariant of the Weyl
curvature tensor best represented by the speciality index , which
gives a 4-dimensional measure of the evolution of the spacetime independent of
all the 3-dimensional gauge-dependent variables except for the time used to
parametrize it. Its graph versus time characterized by correlated isolated
pulses in its real and imaginary parts corresponding to curvature wall
collisions serves as a sort of electrocardiogram of the Mixmaster universe,
with each such pulse pair arising from a single circuit or ``complex pulse''
around the origin in the complex plane. These pulses in the speciality index
and their limiting points on the real axis seem to invariantly characterize
some of the so called spike solutions in inhomogeneous cosmology and should
play an important role as a gauge invariant lens through which to view current
investigations of inhomogeneous Mixmaster dynamics.Comment: version 3: 20 pages iopart style, 19 eps figure files for 8 latex
figures; added example of a transient true spike to contrast with the
permanent true spike example from the Lim family of true spike solutions;
remarks in introduction and conclusion adjusted and toned down; minor
adjustments to the remaining tex
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