arXiv subjects

Gabriel Andres Piovano

Publications and source records attributed to Gabriel Andres Piovano.

12 recordsLinked to original sources

arXiv2026

Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane

We present a family of analytic solutions for the nearly-equatorial motion of a test particle with precessing spin in Kerr spacetime. We solve the equations of motion up to linear order in the small body's spin for periodic and homoclinic orbits. At zero order, the particle moves along equatorial geodesics. The spin-curvature force introduces post-geodesic corrections which, for generic spin orientations, cause the precession of the orbital plane. We derive the solutions for eccentric orbits in terms of Legendre elliptic integrals and Jacobi elliptic functions for generic referential geodesics (known as ``spin gauges"). Our analytical solutions perfectly match the numerical trajectories obtained by Drummond and Hughes in Phys. Rev. D 105, 124041 (2022), and Piovano et al. in Phys. Rev. D 111, 044009 (2025). Furthermore, we present, for the first time, the solutions for homoclinic orbits for a spinning particle in Kerr spacetime, and the spin-corrections to the location of the separatrix. The homoclinic trajectories are described in closed form using elementary functions. Finally, we introduce a novel parametrization for the motion of a spinning particle, called ``fixed eccentricity spin gauge". This is the only spin gauge in which the corrections to periodic orbits are finite at the geodesic separatrix, and continuously reduce to the last stable orbits under appropriate limits. Our results will be useful for modeling the inspiral and transition-to-plunge phases of asymmetric mass binaries within the two-time-scale framework.

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arXiv2026

Shifted-geodesic approximation for spinning-body gravitational wave fluxes

We present a shifted-geodesic framework for computing gravitational-wave fluxes from spinning test bodies moving on bound orbits of Kerr black holes. The method provides a simple and efficient means of evaluating energy and angular momentum fluxes incorporating the leading effect of the smaller body's spin. Because post-adiabatic corrections, including secondary spin contributions, are subdominant to the leading adiabatic terms, this approximation is well justified. In particular, we find that oscillatory spin terms typically contribute very little to fluxes, but their contribution to the description of orbits is computationally expensive, making such terms a natural target for approximation. In our framework, orbital frequencies and integrals of the motion are perturbed to include spin effects, while the trajectory retains the global structure of geodesic motion. This simplifies the computation of gravitational radiation. The shifted-geodesic approximation is most reliable for orbits with lower eccentricity, lower inclination, and larger semi-latus recta. The approximation becomes less reliable as we approach the separatrix between stable and unstable orbits; fortunately, many inspirals spend less time in this region of parameter space. A diagnostic inspiral evolution shows very small dephasing due to use of the shifted-geodesic approximation ($\approx10^{-2}$ radians over 1 year), confirming that spin-induced flux corrections can be accurately included using this simple modification to a geodesic trajectory. This approximation provides a rapid and convenient way to compute spinning-body orbits, but is not intended to replace more accurate treatments. We propose it as a pragmatic alternative when speed and simplicity are prioritized, enabling efficient EMRI/IMRI flux calculations and supporting parameter-space studies for LISA. (Abridged)

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arXiv2026

Going into a tailspin near the abyss: analytic solutions for spinning particles on near equatorial, plunging orbits in Kerr spacetime

This work presents, the first time, analytic solutions for the nearly equatorial, plunging motion of a spinning test-particle in Kerr spacetime. The equations of motion are solved at first-order in the small-body spin for all classes of plunging orbits with energy $E < 1$. The solutions incorporate the small precession of the orbital plane caused by the precession of the particle's spin. Additionally, we present the correction to the radius of the innermost bound circular orbit in closed form, and introduce a novel, Keplerian-like parametrization for generic plunging orbits. Our solutions will be useful in the modelling of inspiral-merger-ringdown waveforms with self-force methods and black hole perturbation theory.

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arXiv2025

Spherical inspirals of spinning bodies into Kerr black holes

Extreme mass-ratio inspirals (EMRIs), consisting of a stellar-mass compact object spiraling into a massive black hole, are key sources for future space-based gravitational wave observatories such as LISA. Accurate modeling of these systems requires incorporating the spin effects of both the primary and secondary bodies, particularly for waveforms at the precision required for LISA detection and astrophysical parameter extraction. In this work, we develop a framework for modeling flux-driven spherical inspirals (orbits of approximately constant Boyer-Lindquist radius) of a spinning secondary into a Kerr black hole. We leverage recently found solutions for the motion of spinning test particles and compute the associated gravitational wave fluxes to linear order in the secondary spin. Next, we show that spherical orbits remain spherical under radiation reaction at linear order in spin, and derive the evolution of the orbital parameters throughout the inspiral. We implement a numerical scheme for waveform generation in the frequency domain and assess the impact of the secondary spin on the gravitational wave signal. In contrast to quasi-circular inspirals, we find that neglecting the secondary spin in spherical inspirals induces large mismatches in the waveforms that will plausibly be detectable by LISA.

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arXiv2025

Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism

Extreme mass-ratio inspirals are among the key sources of gravitational waves for the Laser Interferometer Space Antenna space-based gravitational-wave detector. Achieving sufficient accuracy in the gravitational-wave template for these binaries requires modeling the effects of the spin of the comparably light secondary compact object. In this work, we employ the solution of the Hamilton-Jacobi equations for the motion of spinning bodies in Kerr space-time for the first time to obtain general bound orbits. Specifically, we implement a new solver for the Mathisson-Papapetrou-Dixon equations of motion reduced to first-order form. Our approach provide novel semianalytical expressions for the spin corrections to the orbital motion and frequencies, valid for any choice of referential geodesics, and new analytic expressions for the constants of motion shifts. Then, using the Teukolsky formalism, we compute gravitational-wave energy and angular-momentum fluxes sourced by these orbits valid to linear order in secondary spin and provide waveform snapshots corresponding to the motion. The solver and the novel method we have developed substantially improve on previous studies in terms of speed and accuracy. Additionally, we include the full effect of a general precessing secondary spin in the waveform for the first time. As such, it provides a breakthrough building block for the modeling of waveforms of precessing compact binaries at large mass ratios.

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arXiv2025

Spin-aligned inspiral waveforms from self-force and post-Newtonian theory

We present the state-of-the-art waveform model WaSABI-C for quasicircular inspirals of spinning black hole binaries with aligned or anti-aligned spins. Our model synthesizes the most up-to-date first- and second-order gravitational self-force results with high-order post-Newtonian expansions through a systematic hybridization procedure. This approach captures both strong-field and weak-field dynamics with high fidelity, enabling accurate modeling of spin-(anti)aligned inspirals across a wide parameter space. The resulting waveforms mark a significant advance in the precision of self-force-based templates, providing critical input for the detection and interpretation of gravitational waves from compact binaries with future observatories such as LISA and ET. We accompany this work with the release of WaSABI (Waveform Simulations of Asymmetric Binary Inspirals), a public package implementing our model for community use and further development.

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arXiv2024

Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects

Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions.

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arXiv2024

Accuracy Requirements: Assessing the Importance of First Post-Adiabatic Terms for Small-Mass-Ratio Binaries

We investigate the impact of post-adiabatic (1PA) terms on parameter estimation for extreme and intermediate mass-ratio inspirals using state-of-the-art waveform models. Our analysis is the first to employ Bayesian inference to assess systematic errors for 1PA waveforms. We find that neglecting 1PA terms introduces significant biases for the (small) mass ratio $ε\gtrsim 10^{-5}$ for quasi circular orbits in Schwarzschild spacetime, which can be mitigated with resummed 3PN expressions at 1PA order. Moreover, we show that the secondary spin is strongly correlated with the other intrinsic parameters, and it can not be constrained for $ε\lesssim 10^{-5}$. Finally, we highlight the need for addressing eccentric waveform systematics in the small-mass-ratio regime, as they yield stronger biases than the circular limit in both intrinsic and extrinsic parameters.

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arXiv2022

Extreme Love in the SPA: constraining the tidal deformability of supermassive objects with extreme mass ratio inspirals and semi-analytical, frequency-domain waveforms

We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-based detectors for stellar-mass binaries. Our approach is based on the stationary phase approximation to obtain approximate but accurate semi-analytical EMRI waveforms in the frequency-domain, which greatly speeds up high-precision Fisher-information matrix computations. This approach can be easily extended to several other tests of gravity with EMRIs and to efficiently account for multiple deviations in the waveform at the same time.

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arXiv2021

Assessing the detectability of the secondary spin in extreme mass-ratio inspirals with fully-relativistic numerical waveforms

Extreme mass-ratio inspirals~(EMRIs) detectable by the Laser Inteferometric Space Antenna~(LISA) are unique probes of astrophysics and fundamental physics. Parameter estimation for these sources is challenging, especially because the waveforms are long, complicated, known only numerically, and slow to compute in the most relevant regime, where the dynamics is relativistic. We perform a time-consuming Fisher-matrix error analysis of the EMRI parameters using fully-relativistic numerical waveforms to leading order in an adiabatic expansion on a Kerr background, taking into account the motion of the LISA constellation, higher harmonics, and also including the leading correction from the spin of the secondary in the post-adiabatic approximation. We pay particular attention to the convergence of the numerical derivatives in the Fisher matrix and to the numerical stability of the covariance matrix, which for some systems requires computing the numerical waveforms with approximately $90$-digit precision. Our analysis confirms previous results (obtained with approximated but much more computationally efficient waveforms) for the measurement errors on the binary's parameters. We also show that the inclusion of higher harmonics improves the errors on the luminosity distance and on the orbital angular momentum angles by one order and two orders of magnitude, respectively, which might be useful to identify the environments where EMRIs live. We particularly focus on the measurability of the spin of the secondary, confirming that it cannot be measured with sufficient accuracy. However, due to correlations, its inclusion in the waveform model can deteriorate the accuracy on the measurements of other parameters by orders of magnitude, unless a physically-motivated prior on the secondary spin is imposed.

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arXiv2020

Model independent tests of the Kerr bound with extreme mass ratio inspirals

An outstanding prediction of general relativity is the fact that the angular momentum $S$ of an isolated black hole with mass $μ$ is limited by the Kerr bound, $S\leq Gμ^2/c$. Testing this cornerstone is challenging due to the difficulty in modelling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of $10\%$. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as "superspinars", almost in their entire parameter space.

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arXiv2020

Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion

Extreme mass-ratio inspirals detectable by the future Laser Interferometer Space Antenna provide a unique way to test general relativity and fundamental physics. Motivated by this possibility, here we study in detail the EMRI dynamics in the presence of a spinning secondary, collecting and extending various results that appeared in previous work and also providing useful intermediate steps and new relations for the first time. We present the results of a frequency-domain code that computes gravitational-wave fluxes and the adiabatic orbital evolution for the case of circular, equatorial orbits with (anti)aligned spins. The spin of the secondary starts affecting the gravitational-wave phase at the same post-adiabatic order as the leading-order self-force terms and introduces a detectable dephasing, which can be used to measure it at $5-25\%$ level, depending on individual spins. In a companion paper we discuss the implication of this effect for tests of the Kerr bound.

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