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Giorgio Di Russo

Publications and source records attributed to Giorgio Di Russo.

At least 19 recordsLinked to original sources
arXiv2026

Radiative losses from unbound orbits at quadratic order in spin from MPM formalism

We study the spinning two-body system in the aligned spin case for hyperboliclike motions computing all radiative losses (at the 2PN absolute accuracy and including spin-squared corrections) using the MPM formalism and generalizing previous results valid at linear order in spin [Phys. Rev. D \textbf{108}, no.6, 064049 (2023)]. Leading PM order results are checked against existing literature, whereas higher-order PM results (within the 2PN accuracy) are new with this work. As a by-product of our general results we analyze the spinning situation which supports radial fall (at 2PN and including spin-squared accuracy level contributions), showing that as soon as the PN accuracy increases deviations from radial fall appear necessarily.

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 $ν$, 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

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

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

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↗
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↗
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

Scalar Quasinormal modes in Reissner--Nordström black holes: implications for Weak Gravity Conjecture

Microscopic charged black holes can provide possibilities to test the consistency of the effective field theory (EFT) corrections to Einstein-Maxwell theory. A particularly interesting result is fixing the sign of a certain combination of EFT couplings from the requirement that all charged black holes should be able to evaporate (Weak Gravity Conjecture). In our work, we analysed the EFT corrections to a set of zero-damping quasinormal modes (QNMs) of the scalar wave probe in a nearly extremal Reissner-Nordström black hole. We review the duality of this setup to the problem of the quantum Seiberg-Witten curve of $N=2$ Super-Yang-Mills theory with three flavors. We provide an analytic result for the EFT corrections to the QNMs obtained from the quantization condition imposed on the Seiberg-Witten cycle. Our main result is that the causality requirement of the gravitational theory formulated for the QNMs translates to the same condition on EFT couplings as the one appearing in the Weak Gravity Conjecture.

hep-th↗
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

Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions

We derive formulae that resum, at a given order in the soft limit, the infinite series of Post-Minkowskian (small gravitational coupling) or Post-Newtonian (small velocities) corrections to the gravitational waveform produced by particles moving along a general (open or closed) trajectory in the Schwarzschild geometry in the probe limit. Specifying to the case of circular orbits, we compute the waveform and the energy flux to order 30PN, and compare it against the available results in the literature. Our results are based on a novel hypergeometric representation of the solutions of the Heun equation (and its confluence), that leads to a simple mathematical proof of the Heun connection formula.

gr-qc↗
arXiv2025

Hamiltonian Neural Networks approach to fuzzball geodesics

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential equations capable of describing even complex physical systems is not yet fully widespread in theoretical high-energy physics. Hamiltonian Neural Networks (HNNs) are tools that minimize a loss function defined to solve Hamilton equations of motion. In this work, we implement several HNNs trained to solve, with high accuracy, the Hamilton equations for a massless probe moving inside a smooth and horizonless geometry known as D1-D5 circular fuzzball. We study both planar (equatorial) and non-planar geodesics in different regimes according to the impact parameter, some of which are unstable. Our findings suggest that HNNs could eventually replace standard numerical integrators, as they are equally accurate but more reliable in critical situations.

hep-th↗
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, $ν$, 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↗
arXiv2024

Scalar perturbations in a Top-Star spacetime

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.

gr-qc↗
arXiv2024

Non-spinning tops are stable

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

hep-th↗
arXiv2024

Charge (in)stability and superradiance of Topological Stars

We study linear massive scalar charged perturbations of Topological Stars in the fuzzball and in the black hole (Black String) regimes. The objects that naturally couple to the electric 3-form field strength of these solutions are charged strings, wound around the compact direction. We explore the possibility of instabilities of these solutions, in analogy with the charge instability already highlighted for other non-BPS geometries like JMaRT. This issue is addressed by calculating quasi-normal mode frequencies with a variety of techniques: WKB approximation, direct integration, Leaver method and by exploiting the recently discovered correspondence between black hole-fuzzball perturbation theory and quantum Seiberg-Witten curves. All mode frequencies we find have negative imaginary parts, implying an exponential decay in time. This suggests a linear stability of Topological Stars also in this new scenario. In addition, we study the charge superradiance for the Black String. We compute the amplification factor with the numerical integration method and a quantum Seiberg-Witten motivated definition including instantonic corrections.

hep-th↗