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Fernando de Felice

Publications and source records attributed to Fernando de Felice.

18 recordsLinked to original sources
arXiv2015

The Ray Tracing Analytical Solution within the RAMOD framework. The case of a Gaia-like observer

This paper presents the analytical solution of the inverse ray tracing problem for photons emitted by a star and collected by an observer located in the gravitational field of the Solar System. This solution has been conceived to suit the accuracy achievable by the ESA Gaia satellite (launched on December 19, 2013) consistently with the measurement protocol in General relativity adopted within the RAMOD framework. Aim of this study is to provide a general relativistic tool for the science exploitation of such a revolutionary mission, whose main goal is to trace back star directions from within our local curved space-time, therefore providing a three-dimensional map of our Galaxy. The results are useful for a thorough comparison and cross-checking validation of what already exists in the field of Relativistic Astrometry. Moreover, the analytical solutions presented here can be extended to model other measurements that require the same order of accuracy expected for Gaia.

gr-qc↗
arXiv2014

Observer-dependent optical properties of stationary axisymmetric spacetimes

The world lines of null particles admit arbitrary parametrizations. In the presence of a family of observers one may introduce along a null world line an extension of the so-called Cattaneo's relative standard time parameter (valid for massive particles) which plays a special role. Another possibility is to use the coordinate time itself as a parameter. The relation between relative standard time and coordinate time allows for the introduction of an observer-dependent optical path and associated refraction index. Both these quantities are studied here working out explicit examples concerning familiar null orbits and observers in black hole spacetimes.

gr-qc↗
arXiv2014

The Erez-Rosen metric and the role of the quadrupole on light propagation

The gravitational field of a static body with quadrupole moment is described by an exact solution found by Erez and Rosen. Here we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables like image positions and magnification have been explicitly obtained in the weak field and small quadrupole limit. In this limit the spacetime metric appears as the natural generalization to quadrupole corrections of the metric form adopted also in current astrometric models. Hence, the corresponding analytical solution of the inverse ray tracing problem as well as the consistency with other approaches are also discussed.

gr-qc↗
arXiv2014

Accelerated orbits in black hole fields: the static case

We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of their Frenet-Serret parameters and apply it to explicit cases as those of spatially circular orbits which witness the equilibrium under conflicting types of interactions. In our general analysis we solve the equations of motion offering a detailed picture of the dynamics having in mind a check with a possible astronomical set up. We focus on certain ambiguities which plague the interpretation of the measurements preventing one from identifying the particular structure carried by the particle.

gr-qc↗
arXiv2014

Strains and axial outflows in the field of a rotating black hole

We study the behaviour of an initially spherical bunch of accelerated particles emitted along trajectories parallel to the symmetry axis of a rotating black hole. We find that, under suitable conditions, curvature and inertial strains compete to model the shape of axial outflows of matter contributing to generate jet-like structures. This is of course a purely kinematical effect which does not account by itself for physical processes underlying the formation of jets. In our analysis a crucial role is played by a property of the electric and magnetic part of the Weyl tensor to be Lorentz-invariant boosting along the axis of symmetry in Kerr spacetime.

gr-qc↗
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.

gr-qc↗
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.

gr-qc↗
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.

gr-qc↗
arXiv2008

A generalized Principle of Relativity

In this paper we bring to light an hitherto undisclosed richness of this Theory, namely its admitting a consistent reformulation which is able to provide a unified scenario for all kinds of particles, be they lightlike or not. This result hinges on a "generalized" Principle of Relativity which is {intrinsic} to Einstein's Theory. The road leading to this generalization starts, in the very spirit of Relativity, from enhancing full equivalence between the four spacetime directions by requiring full equivalence between the "motions" along these four spacetime directions as well. So far, no measurable spatial velocity in the direction of the time axis has ever been defined, on the same footing of the usual velocities in the local three-space of a given observer. In this paper, we show how Relativity allows such a "time-velocity" to be defined in a very natural way, for any particle and in any reference frame. As a consequence of this natural definition, it also follows that the time- and space-velocity vectors sum up to define a spacelike "world-velocity" vector, the modulus of which turns out to be equal to the Maxwell's constant c, irrespective of the observer who measures it. This {measurable} world-velocity therefore represents the speed at which "all" kinds of particles move in spacetime, according to any observer. As remarked above, the unifying scenario thus emerging is intrinsic to Einstein's Theory; it extends the role traditionally assigned to Maxwell's constant c, and can therefore justly be referred to as "a generalized Principle of Relativity".

gr-qc↗
arXiv2006

A general relativistic model for the light propagation in the gravitational field of the Solar System: the dynamical case

Modern astrometry is based on angular measurements at the micro-arcsecond level. At this accuracy a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final microarcsecond version of a relativistic astrometric model which enable us to trace back the light path to its emitting source throughout the non-stationary gravity field of the moving bodies in the Solar System. The previous model is used as test-bed for numerical comparisons to the present one. Here we also test different versions of the computer code implementing the model at different levels of complexity to start exploring the best trade-off between numerical efficiency and the micro-arcsecond accuracy needed to be reached.

astro-ph↗
arXiv2005

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.

gr-qc↗
arXiv2004

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 $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ 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.

gr-qc↗
arXiv2004

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 $P$ 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.

gr-qc↗
arXiv2003

Some aspects of Relativistic Astrometry from within the Solar System

In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1-microarcsecond optical observations made by an astrometric satellite orbiting around the Sun. The basic assumption of our model is that the Solar System is the only source of gravity, hence we show how we modeled the satellite observations in a many-body perturbative approach limiting ourselves to the order of accuracy of $(v/c)^2$. The microarcsecond observing scenario outlined is that for the GAIA astrometric mission.

astro-ph↗
arXiv2003

Testing general relativity by micro-arcsecond global astrometry

The global astrometric observations of a GAIA-like satellite were modeled within the PPN formulation of Post-Newtonian gravitation. An extensive experimental campaign based on realistic end-to-end simulations was conducted to establish the sensitivity of global astrometry to the PPN parameter γ, which measures the amount of space curvature produced by unit rest mass. The results show that, with just a few thousands of relatively bright, photometrically stable, and astrometrically well behaved single stars, among the ~10^9 objects that will be observed by GAIA, γcan be estimated after 1 year of continuous observations with an accuracy of ~10^{-5} at the 3σlevel. Extrapolation to the full 5-year mission of these results based on the scaling properties of the adjustment procedure utilized suggests that the accuracy of \simeq 2x10^{-7}, at the same 3σlevel, can be reached with \~10^6 single stars, again chosen as the most astrometrically stable among the millions available in the magnitude range V=12-13. These accuracies compare quite favorably with recent findings of scalar-tensor cosmological models, which predict for γa present-time deviation, |1-γ|, from the General Relativity value between 10^{-5} and 10^{-7}.

astro-ph↗
arXiv1999

Relativistic Charged Spheres II: Regularity and Stability

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already be found (de Felice et al., 1995) but here we generalize that result to cases with different charge distribution within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al. (1998) is incorrect.

gr-qc↗
arXiv1998

Coalescing binary systems of compact objects: Dynamics of angular momenta

The end state of a coalescing binary of compact objects depends strongly on the final total mass M and angular momentum J. Since gravitational radiation emission causes a slow evolution of the binary system through quasi-circular orbits down to the innermost stable one, in this paper we examine the corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or about 0.7(G/c) for the formation of a black hole or a neutron star respectively. The results show cases for which, at the end of the inspiral phase, the conditions for black hole or neutron star formation are not satisfied. The inclusion of spin effects leads us to a study of precession equations valid also for the calculation of gravitational waveforms.

gr-qc↗