7,280 research outputs found
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
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
Circular holonomy in the Taub-NUT spacetime
Parallel transport around closed circular orbits in the equatorial plane of
the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic
monopole parameter on circular holonomy transformations. Investigating the
boost/rotation decomposition of the connection 1-form matrix evaluated along
these orbits, one finds a situation that reflects the behavior of the general
orthogonally transitive stationary axisymmetric case and indeed along Killing
trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure
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
The origins of Causality Violations in Force Free Simulations of Black Hole Magnetospheres
Recent simulations of force-free, degenerate (ffde) black hole magnetospheres
indicate that the fast mode radiated from (or near) the event horizon can
modify the global potential difference in the poloidal direction orthogonal to
the magnetic field, V, in a black hole magnetosphere. There is a fundamental
contradiction in a wave that alters V coming from near the horizon. The
background fields in ffde satisfy the ``ingoing wave condition'' near the
horizon (that arises from the requirement that all matter is ingoing at the
event horizon), yet outgoing waves are radiated from this region in the
simulation. Studying the properties of the waves in the simulations are useful
tools to this end. It is shown that regularity of the stress-energy tensor in a
freely falling frame requires that the outgoing (as viewed globally) waves near
the event horizon are redshifted away and are ineffectual at changing V. It is
also concluded that waves in massless MHD (ffde) are extremely inaccurate
depictions of waves in a tenuous MHD plasma, near the event horizon, as a
consequence black hole gravity. Any analysis based on ffde near the event
horizon is seriously flawed.Comment: 9 pages to appear in ApJ Letter
Spin precession in the Schwarzschild spacetime: circular orbits
We study the behavior of nonzero rest mass spinning test particles moving
along circular orbits in the Schwarzschild spacetime in the case in which the
components of the spin tensor are allowed to vary along the orbit, generalizing
some previous work.Comment: To appear on Classical and Quantum Gravity, 200
Oscillations of the Eddington Capture Sphere
We present a toy model of mildly super-Eddington, optically thin accretion
onto a compact star in the Schwarzschild metric, which predicts periodic
variations of luminosity when matter is supplied to the system at a constant
accretion rate. These are related to the periodic appearance and disappearance
of the Eddington Capture Sphere. In the model the frequency is found to vary
inversely with the luminosity. If the input accretion rate varies (strictly)
periodically, the luminosity variation is quasi-periodic, and the quality
factor is inversely proportional to the relative amplitude of mass accretion
fluctuations, with its largest value approximately Q= 1/(10 |delta Mdot/Mdot|)
attained in oscillations at about 1 to 2 kHz frequencies for a 2 solar mass
star
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