3,068 research outputs found

### Relativistic Gravity Gradiometry: The Mashhoon--Theiss Effect

In general relativity, relativistic gravity gradiometry involves the
measurement of the relativistic tidal matrix, which is theoretically obtained
from the projection of the Riemann curvature tensor onto the orthonormal tetrad
frame of an observer. The observer's 4-velocity vector defines its local
temporal axis and its local spatial frame is defined by a set of three
orthonormal nonrotating gyro directions. The general tidal matrix for the
timelike geodesics of Kerr spacetime has been calculated by Marck\cite{Marck}.
We are interested in the measured components of the curvature tensor along the
inclined "circular" geodesic orbit of a test mass about a slowly rotating
astronomical object of mass $M$ and angular momentum $J$. Therefore, we
specialize Marck's results to such a "circular" orbit that is tilted with
respect to the equatorial plane of the Kerr source. To linear order in $J$, we
recover the Mashhoon--Theiss effect, which is due to a small denominator
("resonance") phenomenon involving the frequency of geodetic precession. The
Mashhoon--Theiss effect shows up as a special long-period gravitomagnetic part
of the relativistic tidal matrix. The physical interpretation of this effect is
briefly discussed.Comment: 23 pages; revtex macros used; two figures; v2: references added,
presentation improved; v3: subsection V(B) added, other additions and
improvement

### Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions

Continuing our analytic computation of the first-order self-force
contribution to Detweiler's redshift variable we provide the exact expressions
of the ninth and ninth-and-a-half post-Newtonian terms.Comment: 4 pages, revtex 4.1 macros use

### Two-body gravitational spin-orbit interaction at linear order in the mass ratio

We analytically compute, to linear order in the mass-ratio, the "geodetic"
spin precession frequency of a small spinning body orbiting a large
(non-spinning) body to the eight-and-a-half post-Newtonian order, thereby
extending previous analytical knowledge which was limited to the third
post-Newtonian level. These results are obtained applying analytical
gravitational self-force theory to the first-derivative level generalization of
Detweiler's gauge-invariant redshift variable. We compare our analytic results
with strong-field numerical data recently obtained by S.~R.~Dolan et al.
[Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order
results capture the strong-field features exhibited by the numerical data. We
argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the
light-ring is approached. We transcribe our kinematical spin-precession results
into a corresponding improved analytic knowledge of one of the two
(gauge-invariant) effective gyro-gravitomagnetic ratios characterizing
spin-orbit couplings within the effective-one-body formalism. We provide
simple, accurate analytic fits both for spin-precession and the effective
gyro-gravitomagnetic ratio. The latter fit predicts that the
linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign
before reaching the light-ring. This strong-field prediction might be important
for improving the analytic modeling of coalescing spinning binaries.Comment: 22 pages, 3 figures, revtex macro

### Peculiar velocities in dynamic spacetimes

We investigate the asymptotic behavior of peculiar velocities in certain
physically significant time-dependent gravitational fields. Previous studies of
the motion of free test particles have focused on the \emph{collapse scenario},
according to which a double-jet pattern with Lorentz factor $\gamma \to \infty$
develops asymptotically along the direction of complete gravitational collapse.
In the present work, we identify a second \emph{wave scenario}, in which a
single-jet pattern with Lorentz factor $\gamma \to \infty$ develops
asymptotically along the direction of wave propagation. The possibility of a
connection between the two scenarios for the formation of cosmic jets is
critically examined.Comment: 17 pages, 1 figure; v2: minor stylistic improvement

### 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

### 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

### 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

### A concise introduction to trapped surface formation in general relativity

Trapped surface formation in general relativity can be studied through a
coupled set of nonlinear equations, where various terms can be neglected, as
was proved by a rigorous mathematical analysis of Christodoulou. This paper is
devoted to a pedagogical synthesis of the mathematical formalism employed in
this analysis, i.e. the optical structure of general relativity investigated by
Christodoulou, Klainerman and other authors after them.Comment: 11 pages. Misprints in Eqs. (1.5), (1.6), (3.24), (3.25) have been
amende

### 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

- β¦