Donato Bini

INO - Istituto Nazionale di Ottica, Florens, Tuscany, Italy

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Publications (191)305.8 Total impact

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    Donato Bini, Bahram Mashhoon
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    ABSTRACT: We study Weitzenb\"ock's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenb\"ock's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we establish along the world line of an arbitrary accelerated observer in general relativity. A similar calculation is carried out in the standard Schwarzschild-like coordinates for static observers in the exterior Kerr spacetime; we then compare our results with the corresponding curvature components. Our work supports the contention that in the extended general relativistic framework involving both the Levi-Civita and Weitzenb\"ock connections, curvature and torsion provide complementary representations of the gravitational field.
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    Donato Bini, Thibault Damour
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    ABSTRACT: 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.
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    ABSTRACT: In light of the relativistic precession model, we present here detailed analyses, extending the ones performed in the Schwarzschild and Kerr spacetimes. We consider the kilohertz quasi-periodic oscillations in the Hartle-Thorne spacetime, which describes the gravitational field of a rotating and deformed object. We derive the analytic formulas for the epicyclic frequencies in the Hartel-Thorne spacetime and by means of these frequencies we interpret the kilohertz quasi-periodic oscillations of low-mass X-ray binaries of the atoll and Z - sources, on the basis of the relativistic precession model. Particularly we perform analyzes for Z -source: GX 5-1. We show that the quasi-periodic oscillations data can provide information on the parameters, namely, the mass, angular momentum and quadrupole moment of the compact objects in the low-mass X-ray binaries.
    Gravitation and Cosmology 12/2014; 20(4). DOI:10.1134/S0202289314040033 · 0.49 Impact Factor
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    Donato Bini, Andrea Geralico
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    ABSTRACT: The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described according to the Mathisson-Papapetrou-Dixon model without any restriction on the motion or simplifying assumption on the associated spin vector and quadrupole tensor, generalizing previous works. The equations of motion are solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables with respect to the characteristic length of the background curvature. The solution provides all corrections to the circular geodesic on the equatorial plane taken as the reference trajectory due to both dipolar and quadrupolar structure of the body as well as the conditions which the nonvanishing components of the quadrupole tensor must fulfill in order that the problem be self-consistent.
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    ABSTRACT: Motivated by the picture of a thin accretion disc around a black hole, radiating mainly in the direction perpendicular to its plane, we study the motion of test particles interacting with a test geodesic radiation flux originating in the equatorial plane of a Schwarzschild space-time and propagating initially in the perpendicular direction. We assume that the interaction with the test particles is modelled by an effective term corresponding to the Thomson-type interaction which governs the Poynting-Robertson effect. After approximating the individual photon trajectories adequately, we solve the continuity equation approximately in order to find a consistent flux density with a certain plausible prescribed equatorial profile. The combined effects of gravity and radiation are illustrated in several typical figures which confirm that the particles are generically strongly influenced by the flux. In particular, they are both collimated and accelerated in the direction perpendicular to the disc, but this acceleration is not enough to explain highly relativistic outflows emanating from some black hole-disc sources. The model can however be improved in a number of ways before posing further questions which are summarized in concluding remarks.
    Monthly Notices of the Royal Astronomical Society 12/2014; 446(3). DOI:10.1093/mnras/stu2242 · 5.23 Impact Factor
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    ABSTRACT: 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.
    Monthly Notices of the Royal Astronomical Society 10/2014; 446(1). DOI:10.1093/mnras/stu2082 · 5.23 Impact Factor
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    Donato Bini, Thibault Damour
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    ABSTRACT: Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme mass-ratio binary systems, to the computation of several tidal invariants. Specifically, we compute, to linear order in the mass ratio and to the 7.5$^{\rm th}$ post-Newtonian order, the following tidal invariants: the square and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric octupolar tidal tensor. Our high-accuracy analytic results are compared to recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja}, and, notably, provide an analytic understanding of the light ring asymptotic behavior found by them. We transcribe our kinematical tidal-invariant results in the more dynamically significant effective one-body description of the tidal interaction energy. By combining, in a synergetic manner, analytical and numerical results, we provide simple, accurate analytic representations of the global, strong-field behavior of the gravitoelectric quadrupolar tidal factor. A striking finding is that the linear-in-mass-ratio piece in the latter tidal factor changes sign in the strong-field domain, to become negative (while its previously known second post-Newtonian approximant was always positive). We, however, argue that this will be more than compensated by a probable fast growth, in the strong-field domain, of the nonlinear-in-mass-ratio contributions in the tidal factor.
    Physical Review D 09/2014; 90(12). DOI:10.1103/PhysRevD.90.124037 · 4.86 Impact Factor
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    ABSTRACT: 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.
    European Physical Journal C 08/2014; 73(2). DOI:10.1140/epjc/s10052-013-2334-9 · 5.44 Impact Factor
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    ABSTRACT: Some strong field effects on test particle motion associated with the propagation of a plane electromagnetic wave in the exact theory of general relativity are investigated. Two different profiles of the associated radiation flux are considered in comparison, corresponding to either constant or oscillating electric and magnetic fields with respect to a natural family of observers. These are the most common situations to be experimentally explored, and have a well known counterpart in the flat spacetime limit. The resulting line elements are determined by a single metric function, which turns out to be expressed in terms of standard trigonometric functions in the case of a constant radiation flux, and in terms of special functions in the case of oscillating flux, leading to different features of test particle motion. The world line deviation between both uncharged and charged particles on different spacetime trajectories due to the combined effect of gravitational and electromagnetic forces is studied. The interaction of charged particles with the background radiation field is also discussed through a general relativistic description of the inverse Compton effect. Motion as well as deviation effects on particles endowed with spin are studied too. Special situations may occur in which the direction of the spin vector change during the interaction, leading to obsevables effects like spin-flip.
    Physical Review D 08/2014; 89(10). DOI:10.1103/PhysRevD.89.104049 · 4.86 Impact Factor
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    Donato Bini, Andrea Geralico
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    ABSTRACT: 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.
    Classical and Quantum Gravity 08/2014; 31(7). DOI:10.1088/0264-9381/31/7/075024 · 3.10 Impact Factor
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    ABSTRACT: 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 the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. 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.
    General Relativity and Gravitation 08/2014; 44(3). DOI:10.1007/s10714-011-1295-2 · 1.73 Impact Factor
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    ABSTRACT: The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state p 0=wρ 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 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 with matter around may offer a new means of gaining insights into the nature of cosmic matter.
    European Physical Journal C 08/2014; 72(3). DOI:10.1140/epjc/s10052-012-1913-5 · 5.44 Impact Factor
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    ABSTRACT: The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
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    Donato Bini, Andrea Geralico
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    ABSTRACT: 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.
    International Journal of Modern Physics D 08/2014; 13(06). DOI:10.1142/S0218271804005031 · 1.42 Impact Factor
  • Physical Review D 08/2014; 90(4). DOI:10.1103/PhysRevD.90.044021 · 4.86 Impact Factor
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    Donato Bini, Bahram Mashhoon
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    ABSTRACT: 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.
    Physical Review D 05/2014; 90(2). DOI:10.1103/PhysRevD.90.024030 · 4.86 Impact Factor
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    Donato Bini, Thibault Damour
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    ABSTRACT: 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.
    Physical Review D 04/2014; 90(2). DOI:10.1103/PhysRevD.90.024039 · 4.86 Impact Factor
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    Donato Bini, Thibault Damour
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    ABSTRACT: We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. We emphasize the increase in \lq\lq transcendentality" of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $\zeta(3)$ (as well as the square of Euler's constant $\gamma$) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u=GM/(c^2r)$ leaves the weak-field domain $u\ll 1$ to enter the strong field domain $u=O(1)$.
    Physical Review D 03/2014; 89(10). DOI:10.1103/PhysRevD.89.104047 · 4.86 Impact Factor
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    ABSTRACT: 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.
    International Journal of Geometric Methods in Modern Physics 03/2014; 11(3). DOI:10.1142/S0219887814500248 · 0.62 Impact Factor
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    Donato Bini, Giampiero Esposito
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    ABSTRACT: Recent work in the literature has found a suppression or, instead, an enhancement of the Cosmic Microwave Background power spectrum in quantum gravity, although the effect is too small to be observed, in both cases. The present paper studies in detail the equations recently proposed for a Born-Oppenheimer-type analysis of the problem. By using a perturbative approach to the analysis of the nonlinear ordinary differential equation obeyed by the two-point function for scalar fluctuations, we find various explicit forms of such a two-point function, with the associated power spectrum. In particular, a new family of power spectra is obtained and studied. The theoretical prediction of power enhancement at large scales is hence confirmed.
    Physical Review D 02/2014; 89(8). DOI:10.1103/PhysRevD.89.084032 · 4.86 Impact Factor

Publication Stats

1k Citations
305.80 Total Impact Points

Institutions

  • 2013–2014
    • INO - Istituto Nazionale di Ottica
      Florens, Tuscany, Italy
  • 2011–2014
    • INFN - Istituto Nazionale di Fisica Nucleare
      Frascati, Latium, Italy
  • 2002–2014
    • National Research Council
      • Institute for Applied Mathematics "Mauro Picone" IAC
      Roma, Latium, Italy
  • 1990–2014
    • Sapienza University of Rome
      • Department of Physics
      Roma, Latium, Italy
  • 1994–2013
    • The American University of Rome
      Roma, Latium, Italy
  • 1998–2011
    • International Center for Relativistic Astrophysics
      Roma, Latium, Italy
  • 1998–2007
    • Villanova University
      • Department of Mathematics and Statistics
      Norristown, Pennsylvania, United States
  • 2004
    • Università degli Studi di Salerno
      • Department of Physics "E. R. Caianiello" DF
      Fisciano, Campania, Italy
  • 2003
    • University of Portsmouth
      • Institute of Cosmology and Gravitation ICG
      Portsmouth, England, United Kingdom