Gianluca Grignani

We determine the metric of a Kerr black hole subject to external tidal fields using metric reconstruction techniques. Working within the Newman-Penrose formalism, we solve the Teukolsky master equation for static, quadrupolar modes associated with a slowly varying tidal environment, and reconstruct the corresponding metric perturbation in the outgoing radiation gauge. As an application, we derive the secular Hamiltonian governing the motion of a test particle in the tidally deformed Kerr spacetime and investigate long-term tidal effects relevant to extreme-mass-ratio inspirals. In particular, we compute tidal-induced shifts of the innermost stable circular orbit and the light ring. We find that these tidal corrections are strongly spin dependent, with significantly larger effects for retrograde orbits around rapidly rotating black holes. Our results provide a fully analytic framework for studying tidal interactions and secular dynamics in rotating black-hole spacetimes, with direct applications to gravitational-wave modeling and tests of gravity in the strong-field regime.

We study hierarchical triple systems formed by a compact binary orbiting a supermassive black hole (SMBH), focusing on the role of relativistic magnetic tidal interactions. Extending previous analyses of precession resonances to 0.5 post-Newtonian order, we incorporate quadrupolar magnetic tidal moments, which have no Newtonian counterpart. We find that magnetic tides introduce new resonances absent at lower order, leading to additional eccentricity excitations and significantly modifying the binary’s long-term evolution. Numerical solutions of the Lagrange planetary equations confirm these analytical predictions and reveal how resonance strength depends on orbital eccentricity and inclination. The resulting dynamics accelerates the binary merger and imprints distinctive signatures on gravitational waves, potentially observable by LISA. Our findings identify magnetic tidal coupling as a novel strong-gravity effect and establish its importance for the resonant dynamics of compact-object binaries near SMBHs.

We derive the gauge-general expressions of the two gyro-gravitomagnetic functions entering the spin-orbit sector of the effective-one-body (EOB) Hamiltonian up to the fifth-and-half post-Newtonian (5.5PN) order. Our results include both local and nonlocal-in-time contributions, providing the most general analytical formulation of the linear-in-spin conservative dynamics within the EOB framework. These expressions are then employed to compute two gauge-invariant observables for quasicircular orbits: the binding energy and the fractional periastron advance. We also use them to compare two spin gauge choices: the well-known Damour-Jaranowski-Schäfer (DJS) gauge, in which the gyro-gravitomagnetic functions are independent of the orbital angular momentum, and the alternative anti-DJS (or DJS ¯ ) gauge, designed to reproduce in the test-mass limit the spin-orbit interaction of a spinning test particle in a Kerr background. For a circular, equal-mass, equal-spin binary, our analysis indicates that the DJS ¯ gauge provides a slightly improved description of the inspiral dynamics, suggesting potential advantages for its use in future EOB waveform models.

The direct current (DC) memory is a non-oscillatory, hereditary component of the gravitational wave (GW) signal that represents one of the most peculiar manifestations of the nonlinear nature of GW emission and propagation. In this work, by transforming the results provided in Ebersold et al. [Phys.Rev.D 100 (2019) 8, 084043] in harmonic coordinates and quasi-Keplerian parametrization, we provide the DC memory in terms of the effective-one-body (EOB) phase-space variables, with a relative accuracy of 2.5PN and in an expansion for small eccentricity up to order six. Our results are then implemented in TEOBResumS-Dalí, thus providing the first EOB model with DC memory contributions. This model is then used to assess the impact on the waveform and the main features of the DC memory, also addressing its dependence on the eccentricity of the binary system at its formation.

We provide the post-Newtonian (PN) waveform for binary systems in motion along generic planar orbits at 2.5PN accuracy, in terms of the dynamical variables of the effective one-body (EOB) formalism. In addition to the calculation of the higher-order terms for all the contributions to the waveform that have been already considered in previous avatars of EOB models, we also compute the EOB expression of the oscillatory memory terms. These are purely noncircular contributions, first appearing at 1.5PN order, that have been so far neglected in the EOB literature. This should foster their inclusion in EOB models and the definitive assessment of their role in shaping gravitational wave signals at infinity. To further promote the application of our results, we also derive associated noncircular factors according to the waveform factorization prescription of the noncircular EOB model TEOBResumS-DALI; the result is a set of ready-to-use noncircular factors that can be directly implemented as extra noncircular corrections in the waveform of TEOBResumS-DALI.

The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this work, for the Kerr black hole, we derive the electric and magnetic tidal moments at quadrupole order, where the latter are computed for the first time in full generality. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extreme-mass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. Our treatment includes strong gravitational effects beyond the post-Newtonian approximation both for the binary system and for the tidal forces since the binary system is allowed to be close to the event horizon of the Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gauge invariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. Our results are relevant for the astrophysical situation in which the binary system is in the vicinity of a supermassive black hole.