arXiv subjects
Publications and source records attributed to Donato Bini.
We study deviations from geodesic motions in a Topological Star spacetime for either massive, charged and spinning particles, elucidating different behaviours with the Schwarzschild spacetime. We also consider the deviations for the motion of electrically charged stringy probes in $D=5$, framing all cases within a unified picture.
After studying properties of the Nariai solution, including its geodesics, in spherical and de Sitter coordinates, two kinds of accelerated motion are investigated in detail: either observers at rest with respect to the coordinates, or observers in radial motion. Next, massless scalar perturbations of Nariai spacetime in absence of sources are worked out, and an explicit example out of the black hole context of analytic self-force calculation is obtained. Last, self-force effects are studied as well, together with some variant of the type of Poynting-Robertson external force, and also building a test electromagnetic field and a test gravitational field in Nariai spacetime geometry
We consider black hole scattering up to the fifth Post Minkowskian ($G^5$) order and compare the predictions of the Tutti Frutti formalism to the results obtained within two different versions of Worldline Effective Field Theory. At the $G^4$ order we highlight the complete agreement between Tutti Frutti results and the results of [C. Dlapa et al., Phys. Rev. Lett. \textbf{130}, no.10, 101401 (2023)], and show how the Tutti Frutti approach allows one to extract the $O(G^3)$ angular momentum loss from the $O(G^4)$ impulse. We compare the sixth Post-Newtonian (6PN) accurate Tutti Frutti predictions to the recent results of [M. Driesse et al., arXiv:2411.11846 [hep-th]], which are at the $G^5$ order, and at the leading order in the two mass ratios, finding complete agreement. We highlight that this agreement involves the presence at the 5.5PN level of a nonlocal tail-of-tail contribution to the scattering (first computed in [D. Bini et al., Phys. Rev. D \textbf{102}, no.8, 084047 (2020)]), and involves, at the 6PN level, the presence of a $O(G^4)$ contribution to the angular momentum loss [C. Heissenberg, arXiv:2501.02904 [hep-th]]. At the second order in the mass ratios of the $O(G^5)$ order we predict two independent gauge-invariant observables to high-PN accuracy.
We study the radiated energy by a scalar particle moving on a circular orbit (smeared in the extra dimension) in the spacetime of a topological star, extending a previous study [Phys. Rev. D {\bf 110}, 084077 (2024)]. We discuss motion in the presence of self-force effects too.
In this paper we present an approach to compute analytical post-Minkowskian corrections to unbound two-body scattering in the self-force formalism. Our method relies on a further low-velocity (post-Newtonian) expansion of the motion. We present a general strategy valid for gravitational and non-gravitational self-force, and we explicitly demonstrate our approach for a scalar charge scattering off a Schwarzschild black hole. We compare our results with recent calculations in [Barack et al., PRD 108, 024025 (2023)], showing complete agreement where appropriate and fixing undetermined scale factors in their calculation. Our results also extend their results by including in our dissipative sector the contributions from the flux into the black hole horizon.
We compute the conservative scattering angle of two classical charged particles at the sixth order in electromagnetic coupling, and at the fourth order in velocity, thereby going beyond the current state of the art [fifth order in coupling, derived by Bern {\it et al.}, Phys. Rev. Lett. \textbf{132}, 251601 (2024)]. Our result is obtained by using the electromagnetic version of the Effective One-Body formalism to transfer information from the exact circular binary-charge solution of Schild [Phys. Rev. \textbf{131}, 2762 (1963)] to the post-Lorentzian expansion of the scattering angle.
The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use our results to check the changes, during scattering, of the individual momenta, as well as of the total angular momentum. High post-Newtonian order values of the $O(G^2)$ radiation-reaction acceleration components are provided for checks of future post-Newtonian computations.
We discuss the dynamics of a (neutral) test particle in Topological Star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the Top-Star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both related to the solutions of a Heun Confluent Equation, but appearing in different contexts in the literature, black hole perturbation theory the first, quantum curves in super-Yang-Mills theories the second.
Using the Multipolar Post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order ($O(G^4)$, or two-loop order), and at the fractional second Post-Newtonian accuracy ($O(v^4/c^4)$). The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, $U_{\ell m}(ω), V_{\ell m}(ω)$, are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked againg existing classical soft theorems. We also complete our previous results on the $O(G^2)$ bremsstrahlung waveform by computing the $O(G^3)$ spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity.
We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically-derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452 [hep-th]], the term quadratic in the amplitude in the observable-based formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h \sim G^1$ and at order $h \sim G^3$ when including disconnected diagrams in the observable-based formalism.
We compute the purely local-in-time (scale-free and logarithm-free) part of the conservative dynamics of gravitationally interacting two-body systems at the fourth post-Minkowskian order, and at the thirtiest order in velocity. The gauge-invariant content of this fourth post-Minkowskian local dynamics is given in two ways: (i) its contribution to the on-shell action (for both hyperboliclike and ellipticlike motions); and (ii) its contribution to the Effective One Body Hamiltonian (in energy gauge). Our computation capitalizes on the Tutti Frutti approach [Phys. Rev. Lett. \textbf{123}, no.23, 231104 (2019)], and on recent post-Minkowskian advances [Phys. Rev. Lett. \textbf{128}, no.16, 161103 (2022)], [Phys. Rev. Lett. \textbf{128}, no.16, 161104 (2022)], and [Phys. Rev. Lett. \textbf{132}, no.22, 221401 (2024)].
We investigate the geometrical properties, spectral classification, geodesics, and causal structure of the Bonnor's spacetime [Journal of Physics A Math. Gen., \textbf{10}, 1673 (1977)], i.e., a stationary axisymmetric solution with a rotating dust as a source. This spacetime has a directional singularity at the origin of the coordinates (related to the diverging vorticity field of the fluid there), which is surrounded by a toroidal region where closed timelike curves (CTCs) are allowed, leading to chronology violations. We use the effective potential approach to provide a classification of the different kind of geodesic orbits on the symmetry plane as well as to study the helical-like motion aroud the symmetry axis on a cylinder with constant radius. In the former case we find that as a general feature for positive values of the angular momentum test particles released from a fixed space point and directed towards the singularity are repelled and scattered back as soon as they approach the CTC boundary, without reaching the central singularity. In contrast, for negative values of the angular momentum there exist conditions in the parameter space for which particles are allowed to enter the pathological region. Finally, as a more realistic mechanism, we study accelerated orbits undergoing friction forces due to the interaction with the background fluid, which may also act in order to prevent particles from approaching the CTC region.
We compare recent one-loop-level, scattering-amplitude-based, computations of the classical part of the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskian waveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$, the two waveforms are found to agree at the Newtonian and first post-Newtonian levels, as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail. However, we find that there are significant differences at the second-and-a-half post-Newtonian level, $O\left( \frac{G^2}{c^5} \right)$, i.e. when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tails of higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines; and (iv) various contributions of cubically nonlinear origin (notably linked to the quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone). These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim ω\ln ω$, i.e. $O\left(\frac{1}{t^2} \right)$ in the time domain. Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checked that they agree with the corresponding existing classical soft graviton results.
We compute the leading order contribution to radiative losses in the case of spinning binaries with aligned spins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through an appropriate spin-orbit modification to the quasi-Keplerian parametrization for nonspinning bodies, which maintains the same functional form, but with spin-dependent orbital elements. We perform consistency checks with existing PN-based and PM-based results. In the former case, we compare our expressions for both radiated energy and angular momentum with those obtained in [JHEP \textbf{04}, 154 (2022)] by applying the boundary-to-bound correspondence to known results for ellipticlike orbits, finding agreement. The linear momentum loss is instead newly computed here. In the latter case, we also find agreement with the low-velocity limit of recent calculations of the total radiated energy, angular momentum and linear momentum in the framework of an extension of the worldline quantum field theory approach to the classical scattering of spinning bodies at the leading post-Minkowskian order [Phys. Rev. Lett. \textbf{128}, no.1, 011101 (2022), Phys. Rev. D \textbf{106}, no.4, 044013 (2022)]. We get exact expressions of the radiative losses in terms of the orbital elements, even if they are at the leading post-Newtonian order, so that their expansion for large values of the eccentricity parameter (or equivalently of the impact parameter) provides higher-order terms in the corresponding post-Minkowskian expansion, which can be useful for future crosschecks of other approaches.
Based on a previous ansatz by Zel'dovich for the gravitational energy of virtual particle-antiparticle pairs, supplemented with the Holographic Principle, we estimate the vacuum energy in a fairly reasonable agreement with the experimental values of the Cosmological Constant. We further highlight a connection between Wheeler's quantum foam and graviton condensation, as contemplated in the quantum $N$-portrait paradigm, and show that such connection also leads to a satisfactory prediction of the value of the cosmological constant. The above results suggest that the "unnaturally" small value of the cosmological constant may find a quite "natural" explanation once the nonlocal perspective of the large $N$-portrait gravitational condensation is endorsed.
The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension four (maximally spanning type I) or dimension three (nonmaximally spanning type I). Explicit examples are provided for both vacuum and nonvacuum spacetimes.
We compute the variation of the Fokker-Wheeler-Feynman total linear and angular momentum of a gravitationally interacting binary system under the second post-Minkowskian retarded dynamics. The resulting $O(G^2)$ equations-of-motion-based, total change in the system's angular momentum is found to agree with existing computations that assumed balance with angular momentum fluxes in the radiation zone.
We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated as gravitational waves in a two-body system undergoing gravitational scattering. We include, for the first time, all the relevant {\it time-asymmetric} effects that arise when consistently going three post Newtonian orders beyond the leading post Newtonian order. We find that the inclusion of time-asymmetric radiative effects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the mass-polynomiality of the post-Minkowskian expansion ($G$ expansion) of the radiated 4-momentum. Imposing the mass-polynomiality of the corresponding individual impulses determines the conservativelike radiative contributions at the fourth post-Minkowskian order, and strongly constrains them at the fifth post-Minkowskian order.