arXiv subjects

Andrea Geralico

Publications and source records attributed to Andrea Geralico.

At least 19 recordsLinked to original sources

arXiv2026

Binary black hole scattering in the extreme-mass-ratio limit: time-domain waveform

The time-domain gravitational waveform emitted during the scattering of two nonspinning compact bodies is computed in the extreme-mass-ratio limit. It provides a time-domain description of the gravitational radiation emitted during the encounter and complements previous first-order self-force calculations, which have primarily been formulated in the frequency domain. In this way, the present results provide a complementary representation of the radiative dynamics and facilitate a direct comparison between time-domain and frequency-domain approaches to the gravitational-wave signal. The waveform is accurate to the fifth post-Minkowskian (three-loop) level and seventh post-Newtonian order, and will serve as a benchmark for future calculations by other methods, to first order in the mass ratio. The results have been already tested in a previous work by constructing the energy and angular momentum fluxes, thereby computing the corresponding radiative losses at the 5PM and 4PM level, respectively, with the same PN accuracy, which are in agreement with recent amplitude-based calculations.

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arXiv2026

High post-Minkowskian gravitational waveform for hyperbolic encounters in the extreme-mass-ratio limit

The frequency-domain waveform emitted by a two-body scattering process is computed in the extreme-mass-ratio limit through the fifth post-Minkowskian (PM) order (i.e., $O(G^5)$) and the fractional sixth post-Newtonian (PN) order. The current accuracy of the scattering waveform obtained by quantum amplitude methods is the one-loop level corresponding to the 3PM order, whereas the 4PM waveform is known up to the 2PN order only as derived within the traditional multipolar-post-Minkowskian formalism. Direct comparison between these waveforms to the first order in the mass ratio shows that they differ at most by the effect of an angular-independent time shift, leading to a complete physical agreement at the same level of accuracy. The new results at the 4PM and 5PM orders thus provide a benchmark for future multiloop calculations. The waveform is also used to obtain the radiated energy at $O(G^6)$, extending it from 3PN to 6PN level.

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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 $\hat U_3(ω, θ,ϕ)$ of $U_3$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_3(ω, θ,ϕ)$. 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.

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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.

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arXiv2026

Gravitational bremsstrahlung waveform at the eighth post-Minkowskian order in the extreme-mass-ratio limit

The gravitational waveform generated by the scattering of two nonspinning bodies is computed in the frequency domain in the extreme-mass-ratio limit at the eighth post-Minkowskian (PM) order (i.e., $O(G^8)$, or six-loop) and at the fractional sixth post-Newtonian (PN) order. Previous results at $O(G^4)$ are completed here by computing the 5PM radiated angular momentum as well as the 6PM radiation-reacted scattering angle. Up to that order the waveform is expressed in terms of few master integrals, with integrands bilinear in (modified) Bessel functions, leading to iterated Bessel functions which can be in turn expressed in terms of Meijer G functions. Starting from $O(G^5)$ (four-loop) the structure of Fourier integrals becomes quite involved. In fact, there are several new families of master integrals, which can be shown to satisfy inhomogeneous Bessel equations with master integrals of lower order as sources. Although limited to the first order in the mass ratio, the results presented here significantly improve the accuracy of the scattering waveform, currently known at the one-loop level from quantum-amplitude-based computations or at the two-loop level (but with 2PN accuracy only) by using the multipolar-post-Minkowskian formalism.

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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, $h(ω, θ,ϕ) \sim G^2 + G^3$. Building on this one-loop-accurate frequency-domain gravitational waveform, we successively derive the spectral gravitational-wave (GW) radiance, $dE^{\rm gw}/(dωdΩ)$, the radiated GW energy spectrum, $dE^{\rm gw}/dω$, and the radiated GW angular distribution, $dE^{\rm gw}/dΩ$, 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).

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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 $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_2(ω, θ,ϕ)$. 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.

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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.

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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.

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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)].

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arXiv2025

Scattering of a point mass by a Schwarzschild black hole: radiated energy and angular momentum

The radiated energy and angular momentum from a point mass on a hyperbolic-like orbit about a Schwarzschild black hole are computed for the first time in the framework of the first-order self-force theory. The analytical expressions for the fluxes are obtained through the standard method of Mano, Suzuki and Takasugi in the form of combined post-Minkowskian (PM) and post-Newtonian (PN) expansions. The reached PM accuracy for the energy and angular momentum losses is $O(G^5)$ and $O(G^4)$, respectively, and 7PN for both. The radiative losses (energy, angular momentum and linear momentum) are currently known in PN-expanded form up to the (fractional) 3PN order [D. Bini et al., Phys. Rev. D \textbf{107}, 024012 (2023)]. Exact PM results valid for arbitrary values of the velocity are limited to $O(G^4)$ for the energy and $O(G^3)$ for the angular momentum. An exact expression for the radiated energy at $O(G^5)$ has been recently obtained in [M. Driesse et al., Nature \textbf{641}, 603-607 (2025)] in the first-order self force limit, whereas the $O(G^4)$ radiated angular momentum has been partially determined in [C. Heissenberg, Phys. Rev. D \textbf{111}, 126012 (2025)]. The results of this work are in agreement with the state of the art of both energy and angular momentum losses, also completing the knowledge of the 4PM radiated angular momentum up to the reached PN accuracy. The expressions for radiative losses are then used to get the 5PM radiation-reacted scattering angle, which should also serve as a cross-check of ongoing calculations by other methods.

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arXiv2024

Post-Minkowskian self-force in the low-velocity limit: scalar field scattering

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.

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arXiv2024

Explicit solution of the gravitational two-body problem at the second post-Minkowskian order

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.

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arXiv2024

Gravitational Bremsstrahlung Waveform at the fourth Post-Minkowskian order and the second Post-Newtonian level

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.

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arXiv2024

Gravitational Waveform: A Tale of Two Formalisms

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.

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arXiv2024

Particle motion in a rotating dust spacetime: the Bonnor solution

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.

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arXiv2024

Comparing One-loop Gravitational Bremsstrahlung Amplitudes to the Multipolar-Post-Minkowskian Waveform

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.

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arXiv2023

Spin-orbit contribution to radiative losses for spinning binaries with aligned spins

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.

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