182 research outputs found

### Observer-dependent tidal indicators in the Kerr spacetime

The observer-dependent tidal effects associated with the electric and
magnetic parts of the Riemann tensor with respect to an arbitrary family of
observers are discussed in a general spacetime in terms of certain "tidal
indicators." The features of such indicators are then explored by specializing
our considerations to the family of stationary circularly rotating observers in
the equatorial plane of the Kerr spacetime. There exist a number of observer
families which are special for several reasons and for each of them such
indicators are evaluated. The transformation laws of tidal indicators when
passing from one observer to another are also discussed, clarifying the
interplay among them. Our analysis shows that no equatorial plane circularly
rotating observer in the Kerr spacetime can ever measure a vanishing tidal
electric indicator, whereas the family of Carter's observers measures zero
tidal magnetic indicator.Comment: 15 pages, 4 figures. Note that there is a misprint in Eq. (4.5) of
the published version: the plus sign in front of the last term in the sum (at
the beginning of the last line) should be a minus sign. The resulting Eq.
(4.6) should be corrected too. However, these misprinted equations are only a
re-writing of previous equations, so that the analysis of the tidal
indicators is not affected. arXiv admin note: text overlap with
arXiv:1306.480

### Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor

The equatorial motion of extended bodies in a Kerr spacetime is investigated
in the framework of the Mathisson-Papapetrou-Dixon model, including the full
set of effective components of the quadrupole tensor. The numerical integration
of the associated equations shows the specific role of the mass and current
quadrupole moment components. While most of the literature on this topic is
limited to spin-induced (purely electric) quadrupole tensor, the present
analysis highlights the effect of a completely general quadrupole tensor on the
dynamics. The contribution of the magnetic-type components is indeed related to
a number of interesting features, e.g., enhanced inward/outward spiraling
behavior of the orbit and spin-flip-like effects, which may have observational
counterparts. Finally, the validity limit of the Mathisson-Papapetrou-Dixon
model is also discussed through explicit examples.Comment: 18 pages, 6 figures; published version. arXiv admin note: text
overlap with arXiv:1311.751

### On the energy content of electromagnetic and gravitational plane waves through super-energy tensors

The energy content of (exact) electromagnetic and gravitational plane waves
is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the
--less familiar-- Chevreton tensors) and natural observers. Starting from the
case of single waves, the more interesting situation of colliding waves is then
discussed, where the nonlinearities of the Einstein's theory play an important
role. The causality properties of the super-momentum four vectors associated
with each of these tensors are also investigated when passing from the
single-wave regions to the interaction region.Comment: 22 pages, 3 figures, iop macros used. Slightly modified version with
respect to the published one: revised quotation of references, new Appendix A
included, typos correcte

### Superposition of Weyl solutions: circular orbits

Circular orbits are examined in static spacetimes belonging to the Weyl class
of vacuum solutions which represent (nonlinear) superposition of the
gravitational fields generated by certain collinear distributions of matter. In
particular, solutions representing two and three Chazy-Curzon particles - all
of them endowed with conical singularities - are considered. Conditions for
geodesic motion in certain symmetry planes are discussed and results are
summarized in a number of graphics too. All the discussion is developed in the
framework of observer-dependent analysis of motion.Comment: 17 pages, 8 figures; published versio

### Dynamics of quadrupolar bodies in a Schwarzschild spacetime

The dynamics of extended bodies endowed with multipolar structure up to the
mass quadrupole moment is investigated in the Schwarzschild background
according to the Dixon's model, extending previous works. The whole set of
evolution equations is numerically integrated under the simplifying assumptions
of constant frame components of the quadrupole tensor and that the motion of
the center of mass be confined on the equatorial plane, the spin vector being
orthogonal to it. The equations of motion are also solved analytically in the
limit of small values of the characteristic length scales associated with the
spin and quadrupole with respect to the background curvature characteristic
length. The results are qualitatively and quantitatively different from
previous analyses involving only spin structures. In particular, the presence
of the quadrupole turns out to be responsible for the onset of a non-zero spin
angular momentum, even if initially absent.Comment: 16 pages, 3 figures; published version. arXiv admin note: substantial
text overlap with arXiv:1311.751

### Relative-observer definition of the Simon tensor

The definition of Simon tensor, originally given only in the Kerr spacetime
and associated with the static family of observers, is generalized to any
spacetime and to any possible observer family. Such generalization is obtained
by a standard "3+1" splitting of the Bianchi identities, which are rewritten
here as a "balance equation" between various spatial fields, associated with
the kinematical properties of the observer congruence and representing the
spacetime curvature.Comment: 19 pages, 1 figure; published versio

### Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime

The deviation from geodesic motion of the world line of an extended body
endowed with multipolar structure up to the mass quadrupole moment is studied
in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The
properties of the quadrupole tensor are clarified by identifying the relevant
components which enter the equations of motion, leading to the definition of an
effective quadrupole tensor sharing its own algebraic symmetries, but also
obeying those implied by the Mathisson-Papapetrou-Dixon model itself. The
equations of motion are then solved analytically in the limit of small values
of the characteristic length scales associated with the spin and quadrupole
variables in comparison with the one associated with the background curvature
and under special assumptions on body's structure and motion. The resulting
quasi-circular orbit is parametrized in a Keplerian-like form, so that
temporal, radial and azimuthal eccentricities as well as semi-major axis,
period and periastron advance are explicitly computed and expressed in terms of
gauge-invariant variables in the weak field and slow motion limit. A companion
numerical study of the equations of motion is performed too.Comment: pages n. 20, fig. n. 1 (n.2 eps files), revtex macro

### Spin-geodesic deviations in the Kerr spacetime

The dynamics of extended spinning bodies in the Kerr spacetime is
investigated in the pole-dipole particle approximation and under the assumption
that the spin-curvature force only slightly deviates the particle from a
geodesic path. The spin parameter is thus assumed to be very small and the back
reaction on the spacetime geometry neglected. This approach naturally leads to
solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables
as well as in the deviation vector, with the same initial conditions as for
geodesic motion. General deviations from generic geodesic motion are studied,
generalizing previous results limited to the very special case of an equatorial
circular geodesic as the reference path.Comment: 19 pages, 6 figures; published versio

### High-energy hyperbolic scattering by neutron stars and black holes

We investigate the hyperbolic scattering of test particles, spinning test
particles and particles with spin-induced quadrupolar structure by a Kerr black
hole in the ultrarelativistic regime. We also study how the features of the
scattering process modify if the source of the background gravitational field
is endowed with a nonzero mass quadrupole moment as described by the
(approximate) Hartle-Thorne solution. We compute the scattering angle either in
closed analytical form, when possible, or as a power series of the
(dimensionless) inverse impact parameter. It is a function of the parameters
characterizing the source (intrinsic angular momentum and mass quadrupole
moment) as well as the scattered body (spin and polarizability constant).
Measuring the scattering angle thus provides useful information to determine
the nature of the two components of the binary system undergoing high-energy
scattering processes.Comment: 12 pages; 2 figures; revtex macros use

### Radiation drag in the field of a non-spherical source

The motion of a test particle in the gravitational field of a non-spherical
source endowed with both mass and mass quadrupole moment is investigated when a
test radiation field is also present. The background is described by the
Erez-Rosen solution, which is a static spacetime belonging to the Weyl class of
solutions to the vacuum Einstein's field equations, and reduces to the familiar
Schwarzschild solution when the quadrupole parameter vanishes. The radiation
flux has a fixed but arbitrary (non-zero) angular momentum. The interaction
with the radiation field is assumed to be Thomson-like, i.e., the particles
absorb and re-emit radiation, thus suffering for a friction-like drag force.
Such an additional force is responsible for the Poynting-Robertson effect,
which is well established in the framework of Newtonian gravity and has been
recently extended to the general theory of relativity. The balance between
gravitational attraction, centrifugal force and radiation drag leads to the
occurrence of equilibrium circular orbits which are attractors for the
surrounding matter for every fixed value of the interaction strength. The
presence of the quadrupolar structure of the source introduces a further degree
of freedom: there exists a whole family of equilibrium orbits parametrized by
the quadrupole parameter, generalizing previous works. This scenario is
expected to play a role in the context of accretion matter around compact
objects.Comment: 12 pages, 5 figures; to appear in MNRA

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