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Donato Bini

Publications and source records attributed to Donato Bini.

At least 19 recordsLinked to original sources
arXiv2026

Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy

Extending our recent work (which focussed on the even-parity quadrupolar part of the waveform), we compute the even-parity octupolar contribution, $U_3$, to the gravitational waveform $W \equiv \frac{c^4 r}{4G} \bar m^{i} \bar m^{j } h_{i j}$ emitted during the scattering of two masses. We work within the Multipolar Post-Minkowskian (MPM) formalism, and use the 3.5 Post-Newtonian (PN) accurate radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We explicitly evaluate the frequency-domain value $\hat U_3(\omega, \theta,\phi)$ of $U_3$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(\omega, \theta,\phi)$, corresponding to $O(G^3)$ contributions to $\hat U_3(\omega, \theta,\phi)$. As a crucial partial confirmation of our result, we find that the 1-loop truncation of our 3.5 PN frequency-domain MPM waveform agrees with corresponding existing Effective Field Theory (EFT) results when taking into account exactly the {\it same} (2.5PN-level) difference in the definitions of the center-of-mass origins within the two formalisms that was deduced from our previous quadrupolar comparison.

gr-qc↗
arXiv2026

Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges

We consider the coordinate-dependent definition of the radiation-reaction force at the third-and-a-half post-Newtonian order for general orbits. In order to (partially) determine its expression we refer to the balance method, involving the energy and angular momentum lost by the system, the Schott terms, and the energy and angular momentum fluxes at infinity. Only the latter are gauge-invariant quantities when passing from a coordinate system to another. The gauge dependence of both radiation-reaction force and Schott terms is encoded in a set of gauge parameters entering their definitions. We show how to relate the harmonic-coordinate losses of mechanical energy and angular momentum by the system with the radial and azimuthal components of the radiation-reaction force in a different coordinate system expressed in terms of phase-space variables in a Hamiltonian framework. The advantage of this approach is that only the coordinate transformation between harmonic coordinates and coordinates and momenta in the new coordinate system is needed, without solving again the balance equations. We derive such a transformation for both Arnowitt-Deser-Misner and Effective-One-Body coordinates. In the latter case we also discuss some simplifying choices of the gauge parameters adopted in current waveform models. Finally, we show how to obtain the solution for the radiation-reaction correction to the orbit in the new coordinate system simply by transforming the harmonic-coordinate solution known in the literature. This is a remarkable simplification, since one can avoid to solve again for the radiation-reacted dynamics.

gr-qc↗
arXiv2026

The radial action for massive particles in spherically symmetric geometries: Exact resummation at any PM order

We compute the massive particles radial action along hyperboliclike geodesics in various spherically symmetric spacetimes: the standard $4d$ Schwarzschild spacetime, its $d$-dimensional genralization known as Schwarzschild-Tangherlini solutions and for the D3-branes spacetimes, showing useful resummation properties in terms of special (hypergeometric, Fox-Wright) functions in the eikonal limit and generalizing previous results valid for null geodesics. As a consequence, the scattering angle can be resummed too, and we explicitly display the resummed expressions. In addition, in the more interesting situation of a $4d$ Schwarzschild black hole spacetime, following the approach of the quantum Seiberg-Witten curves to the radial equation associated with a massive scalar field, we show that the quantum $a$-cycle (or, equivalently, the \lq\lq renormalized angular momentum") is simply related to radial action also in this massive case, providing fully resummed expressions. Finally, we display the explicit, expanded-form expression of the dual $a_D$-cycle, for which, however, no resummed expressions have been derived yet.

gr-qc↗
arXiv2026

5d Schwarzschild-Tangherlini spacetime: MST-like formalism for a Reduced Confluent Heun Equation

We study the five-dimensional Schwarzschild-Tangherlini solution, with particular attention to its geodesic structure and massless scalar perturbations. In the probe limit, we present two applications. First, we compute the scattering angle for unbound geodesics showing both post-Newtonian and post-Minkowskian type expansions, and succeeding in resumming the resulting series in terms of hypergeometric functions. Second, we derive the Lyapunov exponent for deviations from a critical circular orbit, which is relevant to the eikonal estimation of quasinormal modes. We then investigate the dynamics of massless scalar $(s=0)$ perturbations, for which the radial equation becomes a Reduced Confluent Heun equation. In this $d=5$ Schwarzschild-Tangherlini case we develop an original extension of the standard Mano-Suzuki-Takasugi (MST) formalism and validate the construction by computing the renormalized angular-momentum parameter $\nu$, whose value agrees with an independent determination based on the quantum Seiberg-Witten formalism. Finally, we analyze the energy flux from circular orbits, obtaining post-Newtonian results through 2.5PN order.

gr-qc↗
arXiv2026

Radiated Energy Spectrum, Radiated Angular Distribution and Non-linear Memory from the One-loop Gravitational Bremsstrahlung Waveform

The frequency-domain gravitational waveform emitted by the scattering of two non-spinning massive particles has recently been derived at next-to-leading, \textit{i.e.} one-loop, post-Minkowskian order, $h(\omega, \theta,\phi) \sim G^2 + G^3$. Building on this one-loop-accurate frequency-domain gravitational waveform, we successively derive the spectral gravitational-wave (GW) radiance, $dE^{\rm gw}/(d\omega d\Omega)$, the radiated GW energy spectrum, $dE^{\rm gw}/d\omega$, and the radiated GW angular distribution, $dE^{\rm gw}/d\Omega$, up to order $G^4$ included. We deduce from the radiated angular distribution the multipole expansion of the non-linear memory up to order $G^5$ included, thereby extending previous results. We work in the center-of-mass frame, and our results reach the fractional 7.5PN accuracy. For completeness, we include the tree-level information (considered in the center-of-mass frame).

gr-qc↗
arXiv2026

Bekenstein-Hawking temperature from the Schwarzian

Hawking's original derivation of particle creation by black holes in Schwarzschild spacetime exploits, among various concepts, the exponential dependence on the retarded time variable u of the affine parameter \lambda of the null geodesics that are integral curves of the null vector field orthogonal to the Killing horizon. This exponential law implies that the Schwarzian derivative of \lambda with respect to u is minus a half the square of surface gravity. The black hole Killing horizon inherits an intrinsic projective structure, and the squared surface gravity is the invariant characterizing such a structure. There is therefore evidence that the Bekenstein-Hawking temperature is completely determined from the projective structure on the Killing horizon. As a further test, it is here shown that, in a spacetime model with variable mass parameter, the logarithmic derivative of surface gravity is determined by the Schwarzian of the affine parameter. The Schwarzian in Schwarzschild and Kerr geometries is also studied in detail. All these properties are a first step towards proving that black hole thermodynamics finds its mathematical foundations in the projective geometry of Killing horizons. Such a research program can be applied to the power radiated from a black hole, the rate of change of the black hole mass with respect to the area of the event horizon, the fundamental imaginary frequency of quasinormal modes (and hence the decay rate of black hole perturbations).

gr-qc↗
arXiv2026

Gravitational waveform from radial infall at the third-and-half Post-Newtonian order

We compute the gravitational waveform associated with a radially infalling particle in a Schwarzschild black hole working in the center-of-mass system and in a post-Newtonian (PN) approximation. Our results reach the highest accuracy level fully displayed in the literature, namely the 3.5PN order. The latter accuracy includes both conservative and radiation-reaction contributions (at 2.5PN and 3.5PN) in the two-body dynamics, and corresponding effects in the waveform too. The apparent simplicity of the radial fall (namely, the 1-dimensional motion) contrasts with the peculiarity of the process which will end necessarily with the capture of the particle by the black hole, featuring strong field effects. In other words, our analysis being limited to the region of validity of the PN approximation, cannot capture (by definition of PN approximation) the final phase of the fall, but offers significant insights anyway.

gr-qc↗
arXiv2026

Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy

We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(\omega, \theta,\phi)$, corresponding to $O(G^3)$ contributions to $\hat U_2(\omega, \theta,\phi)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames.

gr-qc↗
arXiv2026

Radial fall: the gravitational waveform up to the second-and-half Post-Newtonian order

We consider an application of the Multipolar Post Minkowskian formalism to the case of a two-body system in radial fall. We compute, within the post-Newtonian approximation, the associated gravitational waveform reaching the 2.5 Post-Newtonian accuracy level. At this level the presence of a radiation-reaction force manifests, modifying the fall with a corresponding bremsstrahlung radiation. We evaluate then all emissions: energy, angular momentum (vanishing identically) and linear momentum. We also evaluate the (nonlocal) inertial forces contributions appearing (at the next PN order, 4.5PN) in the center-of-mass due to the losses paving the way for future more accurate computations.

gr-qc↗
arXiv2026

Analytic self-force effects on radial infalling particles in the Schwarzschild spacetime: the radiated energy

We compute, at the first self force accuracy level, the radiated energy from a radially infalling particle released from rest in a Schwarzschild spacetime. We examine both the cases of a scalar particle and that of a massive particle, in the context of gravitational perturbations. Our findings are accompanied by Post-Newtonian checks. In spite of the specific interest for this kind of computations, we outline the building blocks for future higher-order Post-Newtonian computations as well as for extending these results to other interesting situations out of the black hole case.

gr-qc↗
arXiv2025

Scalar self-force effects in neutral $W$-soliton backgrounds

We investigate several geometrical and physical properties of the recently found $W$-soliton solution (neutral case). We discuss both the genuine 5d solution and its reduction to 4d and highlight similarities and differences. In both cases, we study scattering processes of massless and massive particles in the background, reconstructing the gauge-invariant scattering angle, either with exact expressions or with large-angular momentum expansion expressions, which we show how to resum in a useful form. Finally, we analyze the propagation of a test scalar field in the $W$-soliton background and compute the spectrum of Quasi Normal Modes in the case of (non-)minimal coupling and the radiated energy in the case of minimal coupling. Our result for the energy loss is fully analytic and presented in a Post-Newtonian expansion, following the approach termed gravitational self force.

gr-qc↗
arXiv2025

Radiation-reaction correction to scattering binary dynamics at the Next-to-Leading Post-Newtonian Order

We compute the next-to-leading-order radiation-reaction modification to the harmonic coordinate quasi-Keplerian parametrization of the binary dynamics, the two bodies undergoing a scattering process. The solution for the radiation-reaction corrections to the orbital parameters is examined both in the time domain and in the frequency domain. The knowledge of the radiation-reaction corrected orbit is a key ingredient for the calculation of the fractional 3.5PN corrections to the radiative losses as well as to the radiative multipole moments needed to build up the waveform at the same accuracy.

gr-qc↗
arXiv2025

Kerr spacetime and scalar wave equation: Exact resummation of the renormalized angular momentum in the eikonal limit

We show that the null geodesic radial action for unbound orbits in the Kerr spacetime, and consequently the scattering angle, can be resummed in terms of hypergeometric functions, extending previous results [M.~M.~Ivanov, et al. arXiv:2504.07862]. We provide explicit expressions as series expansions in powers of the Kerr rotational parameter up the fourth order included. We finally use the Mano-Suzuki-Takasugi formalism to prove the relation between the renormalized angular momentum and the radial action highlighted in previous works.

gr-qc↗
arXiv2025

High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system

Starting from the recently derived conservative tail-of-tail action [D. Bini and T. Damour, arXiv:2504.20204 [hep-th]] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the 8th post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [A. Geralico, arXiv:2507.03442 [gr-qc]]) with state-of-the-art post-Minkowskian scattering results [M.~Driesse et al., Nature \textbf{641}, no.8063, 603-607 (2025)].

gr-qc↗
arXiv2025

Topological Stars and scalar wave equation: Exact resummation of the renormalized angular momentum in the eikonal limit

We show that for a Topological Star the renormalized angular momentum parameter, $\nu$, appearing in the Mano-Suzuki-Takasugi-type or in the quantum-Seiberg-Witten-type approaches of the perturbation equations, has 1) a direct link with the geodesic radial action computed along the null orbits of the background and 2) admits an exact resummation in terms of hypergeometric functions, generalizing previous results valid in the Schwarzschild case, see Ref.[arXiv:2504.07862 [hep-th]].

gr-qc↗
arXiv2025

Scattering angle in a Topological Star spacetime: a self-force approach

We compute the scattering angle for a scalar neutral probe undergoing unbound motion around a Topological Star, including self-force effects. Moreover we identify the `electro-magnetic' source of the background as Papapetrou Field compatible with the isometries and characterize Topological Stars by studying their sectional curvature, geometric transport along special curves and the gravitational energy content in terms of the super-energy tensors.

gr-qc↗
arXiv2025

High Precision Black Hole Scattering: Tutti Frutti vs Worldline Effective Field Theory

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.

hep-th↗