arXiv subjects

Andrea Geralico

Publications and source records attributed to Andrea Geralico.

At least 127 records · Page 7Linked to original sources

arXiv2014

Frenet-Serret formalism for null world lines

The Frenet-Serret curve analysis is extended from nonnull to null trajectories in a generic spacetime using the Newman-Penrose formalism, recovering old results which are not well known and clarifying the associated Fermi-Walker transport which has been left largely unexplored in the literature. This machinery is then used to discuss null circular orbits in stationary axisymmetric spacetimes using the Kerr spacetime as a concrete example, and to integrate the equations of parallel transport along null geodesics in any spacetime.

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arXiv2014

Strains in General Relativity

The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a "fiducial observer." We find that a relativistically complete and correct definition of strains must take into account the transport law of the chosen spatial triad along the observer's congruence. We use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such a point. The celebrated idea of Szekeres' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles, is here generalized to the case of accelerated particles. In doing so we have naturally contributed to the theory of relativistic gravity gradiometer. Moreover, our analysis was made in an observer-dependent form, a fact that would be very useful when thinking about general relativistic tests on space stations orbiting compact objects like black holes and also in other interesting gravitational situations.

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arXiv2014

Spinning test particles in Weyl spacetimes

The motion of spinning test particles along circular orbits in static vacuum spacetimes belonging to the Weyl class is discussed. Spin alignment and coupling with background parameters in the case of superimposed Weyl fields, corresponding to a single Schwarzschild black hole and single Chazy-Curzon particle as well as to two Schwarzschild black holes and two Chazy-Curzon particles, are studied in detail for standard choices of supplementary conditions. Applications to the gravitomagnetic "clock effect" are also discussed.

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arXiv2014

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.

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arXiv2014

Charged spinning particles on circular orbits in the Reissner-Nordström spacetime

The behaviour of charged spinning test particles moving along circular orbits in the equatorial plane of the Reissner-Nordström spacetime is studied in the framework of the Dixon-Souriau model completed with standard choices of supplementary conditions. The gravitomagnetic " clock effect", i.e. the delay in the arrival times of two oppositely circulating particles as measured by a static observer, is derived and discussed in the cases in which the particles have equal/opposite charge and spin, the latter being directed along the $z$-axis.

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arXiv2013

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.

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arXiv2013

Tidal indicators in the spacetime of a rotating deformed mass

Tidal indicators are commonly associated with the electric and magnetic parts of the Riemann tensor (and its covariant derivatives) with respect to a given family of observers in a given spacetime. Recently, observer-dependent tidal effects have been extensively investigated with respect to a variety of special observers in the equatorial plane of the Kerr spacetime. This analysis is extended here by considering a more general background solution to include the case of matter which is also endowed with an arbitrary mass quadrupole moment. Relation with curvature invariants and Bel-Robinson tensor, i.e., observer-dependent super-energy density and super-Poynting vector, are investigated too.

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arXiv2012

Neutrino oscillations in the field of a rotating deformed mass

The neutrino oscillations in the field of a rotating deformed mass is investigated. The phase shift is evaluated in the case of weak field limit, slow rotation and small deformation. To this aim the Hartle-Thorne metric is used, which is an approximate solution of the vacuum Einstein equations accurate to second order in the rotation parameter $a/M$ and to first order in the mass quadrupole moment $q$. Implications on atmospheric, solar and astrophysical neutrinos are discussed.

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arXiv2011

Spinning bodies and the Poynting-Robertson effect in the Schwarzschild spacetime

A spinning particle in the Schwarzschild spacetime deviates from geodesic behavior because of its spin. A spinless particle also deviates from geodesic behavior when a test radiation field is superimposed on the Schwarzschild background: in fact the interaction with the radiation field, i.e., the absorption and re-emission of radiation, leads to a friction-like drag force responsible for the well known effect which exists already in Newtonian gravity, the Poynting-Robertson effect. Here the Poynting-Robertson effect is extended to the case of spinning particles by modifying the Mathisson-Papapetrou model describing the motion of spinning test particles to account for the contribution of the radiation force. The resulting equations are numerically integrated and some typical orbits are shown in comparison with the spinless case. Furthermore, the interplay between spin and radiation forces is discussed by analyzing the deviation from circular geodesic motion on the equatorial plane when the contribution due to the radiation can also be treated as a small perturbation. Finally the estimate of the amount of radial variation from the geodesic radius is shown to be measurable in principle.

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arXiv2011

de Sitter spacetime: effects of metric perturbations on geodesic motion

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge--Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.

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arXiv2009

Dixon's extended bodies and weak gravitational waves

General relativity considers Dixon's theory as the standard theory to deal with the motion of extended bodies in a given gravitational background. We discuss here the features of the "reaction" of an extended body to the passage of a weak gravitational wave. We find that the body acquires a dipolar moment induced by its quadrupole structure. Furthermore, we derive the "world function" for the weak field limit of a gravitational wave background and use it to estimate the deviation between geodesics and the world lines of structured bodies. Measuring such deviations, due to the existence of cumulative effects, should be favorite with respect to measuring the amplitude of the gravitational wave itself.

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arXiv2009

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein's equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon's model in the gravitational field of a Schwarzschild black hole is discussed. Certain "reciprocity relations" between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon's model for extended bodies in general relativity.

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arXiv2009

Dixon's extended bodies and impulsive gravitational waves

The "reaction" of an extended body to the passage of an exact plane gravitational wave is discussed following Dixon's model. The analysis performed shows several general features, e.g. even if initially absent, the body acquires a spin induced by the quadrupole structure, the center of mass moves from its initial position, as well as certain "spin-flip" or "spin-glitch" effects which are being observed.

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arXiv2009

Quadrupole effects on the motion of extended bodies in Kerr spacetime

The motion of a body endowed with dipolar as well as quadrupolar structure is investigated in the Kerr background according to the Dixon's model, extending a previous analysis done in the Schwarzschild background. The full set of evolution equations is solved under the simplifying assumptions of constant frame components for both the spin and the quadrupole tensors and that the center of mass moves along an equatorial circular orbit, the total four-momentum of the body being aligned with it. We find that the motion deviates from the geodesic one due to the internal structure of the body, leading to measurable effects. Corrections to the geodesic value of the orbital period of a close binary system orbiting the Galactic Center are discussed assuming that the Galactic Center is a Kerr supermassive black hole.

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arXiv2009

Quadrupole effects on the motion of extended bodies in Schwarzschild spacetime

The motion of an extended body up to the quadrupolar structure is studied in the Schwarzschild background following Dixon's model and within certain restrictions (constant frame components for the spin and the quadrupole tensor, center of mass moving along a circular orbit, etc.). We find a number of interesting situations in which deviations from the geodesic motion, due to the internal structure of the particle, can originate measurable effects. However, the standard clock-effect for a pair co/counter-rotating bodies spinning up/down is not modified by the quadrupolar structure of the particle.

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arXiv2009

Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties vs particle motion

An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with arbitrary mass quadrupole moment and is specified by three parameters, the mass $M$, the angular momentum per unit mass $a$ and the quadrupole parameter $q$. It reduces to the Kerr spacetime in the limiting case $q=0$ and to the Erez-Rosen spacetime when the specific angular momentum $a$ vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, turns out to be also a geodesic plane.

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arXiv2008

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 $\mathcal{S}$, 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.

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arXiv2008

Emission vs Fermi coordinates: applications to relativistic positioning systems

A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi triad, as described by the Fermi metric. In the case of a Schwarzschild spacetime modeling the gravitational field around the Earth and an observer at rest at a fixed spacetime point, these coordinates realize a relativistic positioning system alternative to the current GPS system. The latter is indeed essentially conceived as Newtonian, so that it necessarily needs taking into account at least the most important relativistic effects through Post-Newtonian corrections to work properly. Previous results concerning emission coordinates in flat spacetime are thus extended to this more general situation. Furthermore, the mapping between spacetime coordinates and emission coordinates is completely determined by means of the world function, which in the case of a Fermi metric can be explicitly obtained.

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