arXiv subjects
Publications and source records attributed to Donato Bini.
Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi-Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in stationary axisymmetric spacetimes, and illustrated for black hole spacetimes.
A single master equation is given describing spin $s\le2$ test fields that are gauge- and tetrad-invariant perturbations of the {\it spinning C metric} spacetime representing a source with mass $M$, uniformly rotating with angular momentum per unit mass $a$ and uniformly accelerated with acceleration $A$. This equation can be separated into its radial and angular parts. The behavior of the radial functions near the horizons is studied and used to examine the influence of $A$ on the phenomenon of superradiance, while the angular equation leads to modified spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally the coupling between the spin of the perturbing field and the acceleration parameter $A$ is discussed.
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.
The properties of the electric field of a two-body system consisting of a Reissner-Nordström black hole and a charged massive particle at rest have recently been analyzed in the framework of first order perturbation theory following the standard approach of Regge, Wheeler and Zerilli. In the present paper we complete this analysis by numerically constructing and discussing the lines of force of the "effective" electric field of the sole particle with the subtraction of the dominant contribution of the black hole. We also give the total field due to the black hole and the particle. As the black hole becomes extreme an effect analogous to the Meissner effect arises for the electric field, with the "effective field" lines of the point charge being expelled by the outer horizon of the black hole. This effect existing at the level of test field approximation, i.e. by neglecting the backreaction on the background metric and electromagnetic field due to the particle's mass and charge, is here found also at the complete perturbative level. We point out analogies with similar considerations for magnetic fields by Bi{\v c}ák and Dvo{\v r}ák. We also explicitly show that the linearization of the recently obtained Belinski-Alekseev exact solution coincides with our solution in the Regge-Wheeler gauge. Our solution thus represents a "bridge" between the test field solution, which neglects all the feedback terms, and the exact two-body solution, which takes into account all the non-linearity of the interaction.
The \lq\lq effective geometry" formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index $n=1$ is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing in particular on null geodesics as well as on the analog light cone structure.
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.
We discuss geodesic motion in the vacuum C metric using Bondi-like spherical coordinates, with special attention to the role played by the "equatorial plane." We show that the spatial trajectory of photons on such a hypersurface is formally the same of photons on the equatorial plane of the Schwarzschild spacetime, apart from an energy shift involving the spacetime acceleration parameter. Furthermore, we show that photons starting their motion from this hypersurface with vanishing component of the momentum along $θ$, remain confined on it, differently from the case of massive particles. This effect is shown to have a counterpart also in the massless limit of the C metric, i.e. in Minkowski spacetime. Finally, we give the explict map between Bondi-like spherical coordinates and Fermi coordinates (up to the second order) for the world line of an observer at rest at a fixed spatial point of the equatorial plane of the C metric, a result which may be eventually useful to estimate both the mass and the acceleration parameter of accelerated sources.
The circular motion of spinning massive test particles in the equatorial plane of a rotating black hole is investigated in the case in which the components of the spin tensor are allowed to vary along the orbit.
The Frenet-Serret curve analysis is extended from nonnull to null trajectories in a generic spacetime using the Newman-Penrose formalism, recovering old results which are not well known and clarifying the associated Fermi-Walker transport which has been left largely unexplored in the literature. This machinery is then used to discuss null circular orbits in stationary axisymmetric spacetimes using the Kerr spacetime as a concrete example, and to integrate the equations of parallel transport along null geodesics in any spacetime.
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.
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.
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.
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.
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 $γ\to \infty$ 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 $γ\to \infty$ 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.
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.
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.
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 $ζ(3)$ (as well as the square of Euler's constant $γ$) 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 $u=O(1)$.
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.