182 research outputs found

    Observer-dependent tidal indicators in the Kerr spacetime

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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
    corecore