arXiv subjects

Donato Bini

Publications and source records attributed to Donato Bini.

At least 145 records · Page 8Linked to original sources

arXiv2014

Scalar field inflation and Shan-Chen fluid models

A scalar field equivalent to a non-ideal "dark energy fluid" obeying a Shan-Chen-like equation of state is used as the background source of a flat Friedmann-Robertson-Walker cosmological spacetime to describe the inflationary epoch of our universe. Within the slow-roll approximation, a number of interesting features are presented, including the possibility to fulfill current observational constraints as well as a graceful exit mechanism from the inflationary epoch.

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arXiv2014

Friction forces in cosmological models

We investigate the dynamics of test particles undergoing friction forces in a Friedmann-Robertson-Walker (FRW) spacetime. The interaction with the background fluid is modeled by introducing a Poynting-Robertson-like friction force in the equations of motion, leading to measurable (at least in principle) deviations of the particle trajectories from geodesic motion. The effect on the peculiar velocities of the particles is investigated for various equations of state of the background fluid and different standard cosmological models. The friction force is found to have major effects on particle motion in closed FRW universes, where it turns the time-asymptotic value (approaching the recollapse) of the peculiar particle velocity from ultra-relativistic (close to light speed) to a co-moving one, i.e., zero peculiar speed. On the other hand, for open or flat universes the effect of the friction is not so significant, because the time-asymptotic peculiar particle speed is largely non-relativistic also in the geodesic case.

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arXiv2014

Light scattering by radiation fields: the optical medium analogy

The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background field is inhomogeneous and anisotropic in the former case, whereas it is inhomogeneous but isotropic in the latter. The features of light scattering are investigated by assuming the interaction region to be sandwiched between two flat spacetime regions, where light rays propagate along straight lines. Standard tools of ordinary wave optics are used to study the deflection of photon paths due to the interaction with the radiation fields, allowing for a comparison between the optical properties of the equivalent media associated with the different background fields.

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arXiv2014

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.

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arXiv2014

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.

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arXiv2014

The signal from an emitting source moving in a Schwarzschild spacetime under the influence of a radiation field

The motion of matter immersed in a radiation field is affected by radiation drag, as a result of scattering or absorption and re-emission. The resulting friction-like drag, also known as Poynting-Robertson effect, has been recently studied in the general relativistic background of the Schwarzschild and Kerr metric, under the assumption that all photons in the radiation field possess the same angular momentum. We calculate here the signal produced by an emitting point-like specific source moving in a Schwarzschild spacetime under the influence of such a radiation field. We derive the flux, redshift factor and solid angle of the hot spot as a function of (coordinate) time, as well as the time-integrated image of the hot spot as seen by an observer at infinity. The results are then compared with those for a spot moving on a circular geodesic in a Schwarzschild metric.

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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.

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arXiv2014

Scattering of particles by radiation fields: a comparative analysis

The features of the scattering of massive neutral particles propagating in the field of a gravitational plane wave are compared with those characterizing their interaction with an electromagnetic radiation field. The motion is geodesic in the former case, whereas in the case of an electromagnetic pulse it is accelerated by the radiation field filling the associated spacetime region. The interaction with the radiation field is modeled by a force term entering the equations of motion proportional to the 4-momentum density of radiation observed in the particle's rest frame. The corresponding classical scattering cross sections are evaluated too.

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arXiv2014

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.

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arXiv2014

Particle scattering by a test fluid on a Schwarzschild spacetime: the equation of state matters

The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state $p_0= w ρ_0$ is investigated. Deviations from geodesic motion are analyzed as a function of the parameter $w$, ranging from $w=1$ which corresponds to the case of massive free scalar fields, down into the so-called "phantom" energy, with $w<-1$. It is found that the interaction with the fluid distribution leads to capture (escape) of the particle trajectory in the case $1+w>0$ ($<0$), respectively. Based on this result, it is argued that inspection of the trajectories of test particles in the vicinity of a Schwarzschild black hole may offer a new means of gaining insights into the nature of cosmic matter.

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arXiv2014

Spin-geodesic deviations in the Schwarzschild spacetime

The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.

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arXiv2014

Fermi coordinates in Schwarzschild spacetime: closed form expressions

Fermi coordinates are constructed as exact functions of the Schwar\-zschild coordinates around the world line of a static observer in the equatorial plane of the Schwarzschild spacetime modulo a single impact parameter determined implicitly as a function of the latter coordinates. This illustrates the difficulty of constructing explicit exact Fermi coordinates even along simple world lines in highly symmetric spacetimes.

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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.

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arXiv2014

Effect of radiation flux on test particle motion in the Vaidya spacetime

Motion of massive test particles in the nonvacuum spherically symmetric radiating Vaidya spacetime is investigated, allowing for physical interaction of the particles with the radiation field in terms of which the source energy-momentum tensor is interpreted. This "Poynting-Robertson-like effect" is modeled by the usual effective term describing a Thomson-type radiation drag force. The equations of motion are studied for simple types of motion including free motion (without interaction), purely radial and purely azimuthal (circular) motion, and for the particular case of "static" equilibrium; appropriate solutions are given where possible. The results---mainly those on the possible existence of equilibrium positions---are compared with their counterparts obtained previously for a test spherically symmetric radiation field in a vacuum Schwarzschild background.

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arXiv2014

The general relativistic Poynting-Robertson effect. II: A photon flux with nonzero angular momentum

We study the motion of a test particle in a stationary, axially and reflection symmetric spacetime of a central compact object, as affected by interaction with a test radiation field of the same symmetries. Considering the radiation flux with fixed but arbitrary (non-zero) angular momentum, we extend previous results limited to an equatorial motion within a zero-angular-momentum photon flux in the Kerr and Schwarzschild backgrounds. While a unique equilibrium circular orbit exists if the photon flux has zero angular momentum, multiple such orbits appear if the photon angular momentum is sufficiently high.

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arXiv2014

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.

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arXiv2014

Scattering by an electromagnetic radiation field

Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term {\it à la} Poynting-Robertson entering the equations of motion given by the 4-momentum density of radiation observed in the particle's rest frame with a multiplicative constant factor expressing the strength of the interaction itself. Explicit analytical solutions are obtained. Scattering of fields by the electromagnetic wave, i.e., scalar (spin 0), massless spin $\frac12$ and electromagnetic (spin 1) fields, is studied too.

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arXiv2014

The Kerr-Schild ansatz revised

Kerr-Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$, multiplied by some scalar function, say $H$. The basic assumption which led to Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild ansatz is revised by treating Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime. The scalar function $H$ is taken as the perturbing function, so that Einstein's field equations are solved order by order in powers of $H$. It turns out that the congruence must be geodesic and shearfree as a consequence of third and second order equations, leading to an alternative derivation of Kerr solution.

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