arXiv subjects

Donato Bini

Publications and source records attributed to Donato Bini.

At least 91 records · Page 5Linked to original sources

arXiv2018

Scattering by a Schwarzschild black hole of particles undergoing drag force effects

The scattering of massive particles by a Schwarzschild black hole also undergoing a drag force is considered. The latter is modeled as a viscous force acting on the orbital plane, with components proportional to the associated particle 4-velocity components. The energy and angular momentum losses as well as the dependence of the hyperbolic scattering angle on the strength of the drag are investigated in situations where strong field effects cause large deflections.

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arXiv2018

Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole

The scattering of spinning test particles by a Schwarzschild black hole is studied. The motion is described according to the Mathisson-Papapetrou-Dixon model for extended bodies in a given gravitational background field. The equatorial plane is taken as the orbital plane, the spin vector being orthogonal to it with constant magnitude. The equations of motion are solved analytically in closed form to first-order in spin and the solution is used to compute corrections to the standard geodesic scattering angle as well as capture cross section by the black hole.

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arXiv2018

Schwarzschild black hole embedded in a dust field: scattering of particles and drag force effects

A "temporal analogue" of the standard Poynting-Robertson effect is analyzed as induced by a dust of particles (instead of a gas of photons) surrounding a Schwarzschild black hole. Test particles inside this cloud undergo acceleration effects due to the presence of a friction force, so that the fate of their evolution can be completely different from the corresponding geodesic motion. Typical situations are discussed of hyperbolic motion of particles scattered by the black hole in the presence of a dust filling the whole spacetime region outside the horizon as well as particles which free fall radially crossing a corona located at a certain distance from the horizon. The existence of equilibrium orbits may prevent particles from either falling into the hole or escaping to infinity.

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arXiv2018

Relative-observer definition of the Simon tensor

The definition of Simon tensor, originally given only in the Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard "3+1" splitting of the Bianchi identities, which are rewritten here as a "balance equation" between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.

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arXiv2018

Black hole geodesic parallel transport and the Marck recipe for isolating cumulative precession effects

The Wigner rotations arising from the combination of boosts along two different directions are rederived from a relative boost point of view and applied to gyroscope spin precession along timelike geodesics in a Kerr spacetime, clarifying the geometrical properties of Marck's recipe for describing parallel transport along such world lines expressed in terms of the constants of the motion. His final angular velocity isolates the cumulative spin precession angular velocity independent of the spacetime tilting required to keep the spin 4-vector orthogonal to the gyro 4-velocity. As an explicit example the cumulative precession effects are computed for a test gyroscope moving along both bound and unbound equatorial plane geodesic orbits.

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arXiv2018

Gravitational self-force corrections to tidal invariants for particles on circular orbits in a Kerr spacetime

We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order. We then construct the eigenvalues of both electric and magnetic tidal tensors and analytically compute them through high post-Newtonian orders.

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arXiv2018

Tidal invariants along the world line of an extended body in the Kerr spacetime

An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the world line of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction. For example, one can determine the tidal potential in the neighborhood of the body by constructing a body-fixed frame, which requires Fermi-type coordinates attached to the body itself, the latter being in turn related to the spacetime metric and curvature along the considered world line. Similarly, in an effective field theory description of extended bodies finite size effects are taken into account by adding to the point mass action certain non-minimal couplings which involve integrals of tidal invariants along the orbit of the body. In both cases such a computation of tidal tensors is required. Here we consider the case of a spinning body also endowed with a non-vanishing quadrupole moment in a Kerr spacetime. The structure of the body is modeled by a multipolar expansion around the "center of mass line" according to the Mathisson-Papapetrou-Dixon model truncated at the quadrupolar order. The quadrupole tensor is assumed to be quadratic in spin, accounting for rotational deformations. The behavior of tidal invariants of both electric and magnetic type is discussed in terms of gauge-invariant quantities when the body is moving along a circular orbit as well as in the case of an arbitrary (equatorial) motion. The analysis is completed by examining the associated eigenvalues and eigenvectors of the tidal tensors. The limiting situation of the Schwarzschild solution is also explored both in the strong field regime and in the weak field limit.

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arXiv2018

Gravitational self-force corrections to tidal invariants for particles on eccentric orbits in a Schwarzschild spacetime

We study tidal effects induced by a particle moving along a slightly eccentric equatorial orbits in a Schwarzschild spacetime within the gravitational self-force framework. We compute the first order (conservative) corrections in the mass-ratio to the eigenvalues of the electric-type and magnetic-type tidal tensors up to the second order in eccentricity and through the 9.5 post-Newtonian order. Previous results on circular orbits are thus generalized and recovered in a proper limit.

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arXiv2018

Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime

We compute gravitational self-force corrections to tidal invariants for spinning particles moving along circular orbits in a Schwarzschild spacetime. In particular, we consider the square and the cube of the gravitoelectric quadrupolar tidal tensor and the square of the gravitomagnetic quadrupolar tidal tensor. Our results are accurate to first-order in spin and through the 9.5 post-Newtonian order. We also compute the associated electric-type and magnetic-type eigenvalues.

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arXiv2018

High-energy hyperbolic scattering by neutron stars and black holes

We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.

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arXiv2018

Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation

We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second-order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced in Phys. Rev. D {\bf 96}, 104038 (2017), we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the Effective One-Body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.

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arXiv2018

On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds

We study trapped surfaces from the point of view of local isometric embedding into three-dimensional Riemannian manifolds. When a two-surface is embedded into three-dimensional Euclidean space, the problem of finding all surfaces applicable upon it gives rise to a non-linear partial differential equation of Monge-Ampere type, first discovered by Darboux, and later reformulated by Weingarten. Even today, this problem remains very difficult, despite some remarkable results. We find an original way of generalizing the Darboux technique, which leads to a coupled set of 6 non-linear partial differential equations. For the 3-manifolds occurring in Friedmann-(Lemaitre)-Robertson-Walker cosmologies, we show that the local isometric embedding of trapped surfaces into them can be proved by solving just one non-linear equation. Such an equation is here solved for the three kinds of Friedmann model associated with positive, zero, negative curvature of spatial sections, respectively.

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arXiv2018

Twisted Gravitational Waves

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

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arXiv2018

Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the $z$-axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.

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arXiv2018

Spin-orbit precession along eccentric orbits: improving the knowledge of self-force corrections and of their effective-one-body counterparts

The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth post-Newtonian order, improving recent results by Kavanagh et al. [Phys.\ Rev.\ D {\bf 96}, 064012 (2017).] This information is then converted into its corresponding Effective-One-Body counterpart, thereby determining several new post-Newtonian terms in the gyrogravitomagnetic ratio $g_{S*}$.

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arXiv2017

Anisotropic Gravitational Collapse and Cosmic Jets

Consider a dynamic general relativistic spacetime in which the proper infinitesimal interval along one spatial coordinate direction decreases monotonically with time, while the corresponding intervals increase along other spatial directions. In a system undergoing such complete anisotropic collapse/expansion, we look for the formation of a cosmic double-jet configuration: free test particles in the ambient medium, relative to the collapsing system, gain energy from the gravitational field and asymptotically line up parallel and antiparallel to the direction of collapse such that their Lorentz factors approach infinity. A strong burst of electromagnetic radiation is expected to accompany this event if some of the free test particles carry electric charge. Previous work in this direction involved mainly Ricci-flat spacetimes; hence, we concentrate here on inhomogeneous perfect fluid spacetimes. We briefly explore the possible connection between these theoretical cosmic jets and astrophysical jets. We also discuss other general relativistic scenarios for the formation of cosmic jets.

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arXiv2017

Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory

A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e. first order in $G$ and all orders in $v/c$), of the values of the two gyrogravitomagnetic ratios describing spin-orbit coupling in the Effective One-Body formalism. These gyrogravitomagnetic ratios are found to tend to zero in the ultrarelativistic limit.

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arXiv2017

Hyperbolic scattering of spinning particles by a Kerr black hole

We investigate the scattering of a spinning test particle by a Kerr black hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The particle's spin and orbital angular momentum are taken to be aligned with the black hole's spin. Both the particle's mass and spin length are assumed to be small in comparison with the characteristic length scale of the background curvature, in order to avoid backreaction effects. We analytically compute the modifications due to the particle's spin to the scattering angle, the periastron shift, and the condition for capture by the black hole, extending previous results valid for the nonrotating Schwarzschild background. Finally, we discuss how to generalize the present analysis beyond the linear approximation in spin, including spin-squared corrections in the case of a black-hole-like quadrupolar structure for the extended test body.

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