Donato Bini

INFN - Istituto Nazionale di Fisica Nucleare, Frascati, Latium, Italy

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Publications (177)264.9 Total impact

  • 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). · 3.56 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.
    08/2014;
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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). · 5.25 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). · 1.90 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). · 5.25 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.
    08/2014;
  • 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.
    08/2014;
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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.
    04/2014;
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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 $u=O(1)$.
    03/2014;
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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.
    02/2014; 89(8).
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    ABSTRACT: A non-ideal 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. The usual formulation in terms of a self-interacting scalar field in an external potential is developed, completely determined by the Shan-Chen energy density and pressure. Within the slow-roll approximation, a number of interesting features are presented, including the possibility to fulfill current observational constraints. Furthermore, this model provides a natural exit mechanism from the inflationary epoch.
    01/2014;
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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 01/2014; 11(3). · 0.95 Impact Factor
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    ABSTRACT: The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.
    General Relativity and Gravitation 01/2014; 46(1). · 1.90 Impact Factor
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    Donato Bini, Thibault Damour
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    ABSTRACT: We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio 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. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.
    12/2013; 89(6).
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    Donato Bini, Andrea Geralico
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    ABSTRACT: 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.
    11/2013; 89(4).
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    ABSTRACT: We consider a Friedmann-Robertson-Walker universe with a fluid source obeying a nonideal equation of state with ‘‘asymptotic freedom,” namely ideal gas behavior (pressure changes directly proportional to density changes) both at low and high density regimes, following a fluid dynamical model due to Shan and Chen. It is shown that, starting from an ordinary energy density component, such fluids naturally evolve towards a universe with a substantial ‘‘dark energy” component at the present time, with no need of invoking any cosmological constant. Moreover, we introduce a quantitative indicator of darkness abundance, which provides a consistent picture of the actual matter-energy content of the Universe.
    Physical Review D 09/2013; 88(6). · 4.69 Impact Factor
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    ABSTRACT: We investigate the influence of the quadrupole moment of a rotating source on the motion of a test particle in the strong field regime. For this purpose the Hartle-Thorne metric, that is an approximate solution of vacuum Einstein field equations that describes the exterior of any slowly rotating, stationary and axially symmetric body, is used. The metric is given with accuracy up to the second order terms in the body's angular momentum, and first order terms in its quadrupole moment. We give, with the same accuracy, analytic equations for equatorial circular geodesics in the Hartle-Thorne spacetime and integrate them numerically.
    06/2013;
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    Donato Bini, Thibault Damour
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    ABSTRACT: We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a_5 (nu) - a_5 (0) is deduced from recent results of Jaranowski and Sch\"afer, and is found to be significantly negative.
    Physical review D: Particles and fields 05/2013; 87(12).
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    ABSTRACT: 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.
    EPL (Europhysics Letters) 05/2013; 102(2):20006. · 2.26 Impact Factor
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    ABSTRACT: We evaluate the modifications to the cosmic microwave background anisotropy spectrum that result from a semiclassical expansion of the Wheeler-DeWitt equation. Recently, such an investigation in the case of a real scalar field coupled to gravity, has led to the prediction that the power at large scales is suppressed. We make here a more general analysis and show that there is an ambiguity in the choice of solution to the equations describing the quantum gravitational effects. Whereas one of the two solutions describes a suppression of power, the other one describes an enhancement. We investigate possible criteria for an appropriate choice of solution. The absolute value of the correction term is in both cases of the same order and currently not observable. We also obtain detailed formulae for arbitrary values of a complex parameter occurring in the general solution of the nonlinear equations of the model. We finally discuss the modification of the spectral index connected with the power spectrum and comment on the possibility of a quantum-gravity induced unitarity violation.
    Physical review D: Particles and fields 03/2013; 87(10).

Publication Stats

806 Citations
264.90 Total Impact Points

Institutions

  • 2014
    • INFN - Istituto Nazionale di Fisica Nucleare
      Frascati, Latium, Italy
  • 1990–2014
    • Sapienza University of Rome
      • Department of Physics
      Roma, Latium, Italy
  • 1994–2013
    • The American University of Rome
      Roma, Latium, Italy
  • 2011
    • LIUCBM Libera Università Campus Bio-Medico di Roma
      Roma, Latium, Italy
  • 2000–2011
    • Villanova University
      • Department of Mathematics and Statistics
      Norristown, Pennsylvania, United States
  • 1998–2010
    • International Center for Relativistic Astrophysics
      Roma, Latium, Italy
  • 2003
    • University of Portsmouth
      • Institute of Cosmology and Gravitation ICG
      Portsmouth, England, United Kingdom