arXiv subjects

Georgios Lukes-Gerakopoulos

Publications and source records attributed to Georgios Lukes-Gerakopoulos.

At least 19 recordsLinked to original sources

arXiv2026

Spinning charged test particle dynamics around a Schwarzschild black hole embedded in a homogeneous magnetic field

We study the dynamics of spinning charged test particles orbiting a Schwarzschild black hole immersed in a test uniform magnetic field. This setup provides a simple but physically relevant framework for modeling particle motion in magnetized astrophysical environments near compact objects, where both spin-curvature coupling and electromagnetic interactions can play a significant role. The particle trajectories are obtained numerically in both equatorial and off-equatorial configurations, allowing us to examine the influence of spin-curvature and Lorentz forces on the motion. In the equatorial plane, assuming the particle's spin vector is orthogonal to the orbital plane, we derive analytical expressions for the conserved energy and angular momentum, as well as for the radial and orbital frequencies as functions of spin parameter and magnetic parameter. We also construct the corresponding effective potential to determine the allowed regions of particle motion. The equatorial dynamics remain integrable due to the existence of conserved quantities associated with the spacetime symmetries and the alignment of the magnetic field. In contrast, the off-equatorial motion constitutes a non-integrable dynamical system. While limiting subcases of the system, i.e., the spinning neutral and non-spinning charged cases, can be analyzed using two-dimensional Poincaré surface of sections (PSs), the combined system can be reduced only up to three degrees of freedom. Hence, to investigate the resulting complexity, we analyze the phase space using four-dimensional PS along with recurrence analysis, revealing the presence of chaotic behavior for particular choices of parameters and initial conditions. Finally, we compare the dynamics of spinning charged test particles with the limiting cases, thereby distinguishing the respective contributions of spin-curvature and electromagnetic interactions.

gr-qc↗

arXiv2026

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

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arXiv2025

Extreme mass ratio inspirals into black holes surrounded by matter: Resonance crossings

The forthcoming space-based gravitational-wave observatory Laser Interferometer Space Antenna (LISA) should enable the detection of Extreme Mass Ratio Inspirals (EMRIs), in which a stellar-mass compact object gradually inspirals into a supermassive black hole while emitting gravitational waves. Modeling the waveforms of such systems is a challenging task, requiring precise computation of energy and angular momentum fluxes as well as proper treatment of orbital resonances, during which two fundamental orbital frequencies become commensurate. In this work, we perform a systematic comparison of fluxes derived from three approaches: the quadrupole formula, post-Newtonian approximations, and time-domain solutions of the Teukolsky equation. We show that quadrupole-based fluxes remain in good agreement with Teukolsky results across a broad range of orbital configurations, including perturbed orbits. Building on these insights, we explore the dynamical impact of resonance crossings within the adiabatic approximation. By introducing novel numerical methods, we reduce computational costs and uncover diverse resonance-crossing behaviors. These results contribute to the effort to understand theoretically and model adequately resonance crossings during an EMRI.

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arXiv2025

Circular equatorial orbits of extended bodies with spin-induced quadrupole around a Kerr black hole: Comparing spin-supplementary conditions

The worldline of an extended body in curved spacetime can be described by the Mathisson-Papapetrou-Dixon equations when its centroid, i.e., its center of mass, is fixed by a spin supplementary condition (SSC). Different SSC choices result in distinct worldlines. To examine the properties of these choices, we investigate the frequency of circular equatorial orbits of extended bodies within the pole-dipole-(spin-induced) quadrupole approximation moving around a Kerr black hole for the Tulzcyjew-Dixon (TD) and the Mathisson-Pirani (MP) SSCs. First, we examine similarities and discrepancies in the prograde and retrograde orbital frequencies by expanding these frequencies in power series of the spin without taking into account the fact that both the position of the centroid and the spin measure change under the transition from one SSC to another. Then, by taking into account the centroid transition laws we examine the orbital frequencies convergence between the non-helical MP frame to the TD frame. In particular, we demonstrate that, in analogy to the pole-dipole approximation, the transition from one circular orbit to another within the pole-dipole-(spin-induced)quadrupole approximation under a change in the SSC, results in convergence between the SSCs only up to certain terms in the spin expansion and does not extend to the entire power series. Finally, we discuss the innermost stable circular orbits (ISCOs) in the pole-dipole-(spin-induced)quadrupole approximation under TD and MP SSCs.

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arXiv2024

Combining Machine Learning with Recurrence Analysis for resonance detection

The width of a resonance in a nearly integrable system, i.e. in a non-integrable system where chaotic motion is still not prominent, can tell us how a perturbation parameter is driving the system away from integrability. Although the tool that we are presenting here can be used is quite generic and can be used in a variety of systems, our particular interest lies in binary compact object systems known as extreme mass ratio inspirals (EMRIs). In an EMRI a lighter compact object, like a black hole or a neutron star, inspirals into a supermassive black hole due to gravitational radiation reaction. During this inspiral the lighter object crosses resonances, which are still not very well modeled. Measuring the width of resonances in EMRI models allows us to estimate the importance of each perturbation parameter able to drive the system away from resonances and decide whether its impact should be included in EMRI waveform modeling or not. To tackle this issue in our study we show first that recurrence quantifiers of orbits carry imprints of resonant behavior, regardless of the system's dimensionality. As a next step, we apply a long short-term memory machine learning architecture to automate the resonance detection procedure. Our analysis is developed on a simple standard map and gradually we extend it to more complicated systems until finally we employ it in a generic deformed Kerr spacetime known in the literature as the Johannsen-Psaltis spacetime.

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arXiv2024

Comparing effective-one-body and Mathisson-Papapetrou-Dixon results for a spinning test particle on circular equatorial orbits around a Kerr black hole

We consider a spinning test particle around a rotating black hole and compare the Mathisson-Papapetrou-Dixon (MPD) formalism under the Tulczyjew-Dixon spin supplementary condition to the test-mass limit of the effective-one-body (EOB) Hamiltonian of [Phys. Rev. D.90, 044018(2014)], with enhanced spin-orbit sector. We focus on circular equatorial orbits: we first compare the constants of motion at their linear in secondary spin approximation and then we compute the gravitational-wave (GW) fluxes using a frequency domain Teukolsky equation solver. We find no difference between the EOB and MPD fluxes when the background spacetime is Schwarzschild, while the difference for a Kerr background is maximum for large, positive spins. Our work could be considered as a first step to improve the radiation reaction of the EOB model, in view of the needs of the next-generation of GW detectors.

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arXiv2024

Comparing second-order gravitational self-force and effective-one-body waveforms from inspiralling, quasi-circular black hole binaries with a non-spinning primary and a spinning secondary

We present the first comparison of waveforms evaluated using the effective-one-body (EOB) approach and gravitational self-force (GSF) theory for inspiralling black hole binaries with a non-spinning primary and a spinning secondary. This paper belongs to a series of papers comparing the EOB model TEOBResumS to GSF results, where the latter are used to benchmark the EOB analytical choices in the large-mass-ratio regime. In this work, we explore the performance of two gauge choices for the gyro-gravitomagnetic functions GS, GS* entering the spin-orbit sector within the EOB dynamics. In particular, we consider the usual gauge of TEOBResumS, where GS and GS* only depend on the inverse radius and the radial momentum, and a different gauge where these functions also depend on the azimuthal momentum. The latter choice allows us to exploit as prefactor in GS* the complete expression GKS* for a spinning particle on Kerr. As done previously, we employ both waveform alignments in the time domain and a gauge-invariant frequency-domain analysis to gain a more complete understanding of the impact of the new analytical choice. The frequency-domain analysis is particularly useful in confirming that the gyro-gravitomagnetic functions in the new chosen gauge bring the EOB spin contribution at 1st post-adiabatic order closer to the GSF one. We finally implement the improved functions within the public code for TEOBResumS-Dalí, which already incorporates eccentricity. In this way, we upgrade the EOB model for extreme-mass-ratio inspirals presented in our previous work.

gr-qc↗

arXiv2024

Detectability of stochastic gravitational wave background from weakly hyperbolic encounters

We compute the stochastic gravitational wave (GW) background generated by black hole-black hole (BH-BH) hyperbolic encounters with eccentricities close to one and compare them with the respective sensitivity curves of planned GW detectors. We use the Keplerian potential to model the orbits of the encounters and the quadrupole formula to compute the emitted GWs. We take into account hyperbolic encounters that take place in clusters up to redshift $5$ and with BH masses spanning from $5 M_{\odot}$ to $55 M_{\odot}$. We assume the clusters to be virialized and study several cluster models with different mass and virial velocity, and finally obtain an accumulative result, displaying the background as an average. Using the maxima and minima of our accumulative result for each frequency, we provide analytical expressions for both optimistic and pessimistic scenarios. Our results suggest that the background from these encounters is likely to be detected by the third-generation detectors Cosmic explorer and Einstein telescope, while the tail section at lower frequencies intersects with DECIGO, making it a potential target source for both ground- and space-based future GW detectors.

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arXiv2024

A deep classifier of chaos and order in Hamiltonian systems of two degrees of freedom

Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of classifying chaos from order in the discretised dynamics of Hamiltonian systems of two degrees of freedom, through the machinery of Poincaré maps. Our deep network is based predominantly on a convolutional architecture, and generalises with good accuracy on unseen datasets, thanks to the universal features of a perturbed pendulum learned by the deep network. We discuss in detail the significance and the preparation of our training set, and we showcase how our deep network can be applied to the dynamics of geodesic motion in an axi-symmetric and stationary spacetime of a compact object deviating from the Kerr black hole paradigm. Finally, we discuss current challenges and some promising future directions.

nlin.AO↗

arXiv2023

Can extended bodies follow geodesic trajectories?

We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee, S., Lukes-Gerakopoulos, G. and Nayak, R. K. (2022), Extended bodies moving on geodesic trajectories, General Relativity and Gravitation, 54(9), 113, arXiv: 1907.05659. In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semerák spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can take place also in the pole-dipole-quadrupole approximation, when only the mass quadrupole is taken into account. For our analysis we employ the assumption that the dipole contribution and the quadrupole contribution vanish independently.

gr-qc↗

arXiv2023

Growth of orbital resonances around a black hole surrounded by matter

This work studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric distribution of mass enclosing the system. This spacetime can serve as a versatile model for a diverse range of astrophysical scenarios and, in particular, for extreme mass ratio inspirals as in our work. We show that the system is non-integrable by employing Poincaré surface of section and rotation numbers. By utilising the rotation numbers, the widths of resonances are calculated, which are then used in establishing the relation between the underlying perturbation parameter driving the system from integrability and the quadrupole parameter characterising the perturbed metric. This relation allows us to estimate the phase shift caused by the resonance during an inspiral.

gr-qc↗

arXiv2023

The Laser Interferometer Space Antenna mission in Greece White Paper

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the mid-2030s, is a gravitational wave observatory in space designed to detect sources emitting in the millihertz band. LISA is an ESA flagship mission, currently entering the Phase B development phase. It is expected to help us improve our understanding about our Universe by measuring gravitational wave sources of different types, with some of the sources being at very high redshifts $z\sim 20$. On the 23rd of February 2022 we organized the 1$^\mathrm{st}$ {\it LISA in Greece Workshop}. This workshop aimed to inform the Greek scientific and tech industry community about the possibilities of participating in LISA science and LISA mission, with the support of the Hellenic Space Center (HSC). In this white paper, we summarize the outcome of the workshop, the most important aspect of it being the inclusion of $15$ Greek researchers to the LISA Consortium, raising our total number to $22$. At the same time, we present a road-map with the future steps and actions of the Greek Gravitational Wave community with respect to the future LISA mission.

gr-qc↗

arXiv2023

Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime

We introduce an action-angle formalism for bounded geodesic motion in Kerr black hole spacetime using canonical perturbation theory. Namely, we employ a Lie series technique to produce a series of canonical transformations on a Hamiltonian function describing geodesic motion in Kerr background written in Boyer-Lindquist coordinates to a Hamiltonian system written in action-angle variables. This technique allows us to produce a closed-form invertible relation between the Boyer-Lindquist variables and the action-angle ones, while it generates in analytical closed form all the characteristic functions of the system as well. The expressed in the action-angle variable Hamiltonian system is employed to model an extreme mass ratio inspiral (EMRI), i.e. a binary system where a stellar compact object inspirals into a supermassive black hole due to gravitational radiation reaction. We consider the adiabatic evolution of an EMRI, for which the energy and angular momentum fluxes are computed by solving the Teukolsky equation in the frequency domain. To achieve this a new Teukolsky equation solver code was developed.

gr-qc↗

arXiv2023

Extreme mass ratio inspirals into black holes surrounded by matter

Inspirals of stellar-mass compact objects into massive black holes, known as extreme mass ratio inspirals (EMRIs), are one of the key targets for upcoming space-based gravitational-wave detectors. In this paper we take the first steps needed to systematically incorporate the effect of external gravitating matter on EMRIs. We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass. Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties. This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.

gr-qc↗

arXiv2023

Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime

This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit four-velocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC.

gr-qc↗

arXiv2023

Asymptotic gravitational-wave fluxes from a spinning test body on generic orbits around a Kerr black hole

This work provides gravitational wave energy and angular momentum asymptotic fluxes from a spinning body moving on generic orbits in a Kerr spacetime up to linear in spin approximation. To achieve this, we have developed a new frequency domain Teukolsky equation solver that calculates asymptotic amplitudes from generic orbits of spinning bodies with their spin aligned with the total orbital angular momentum. However, the energy and angular momentum fluxes from these orbits in the linear in spin approximation are appropriate for adiabatic models of extreme mass ratio inspirals even for spins non-aligned to the orbital angular momentum. To check the newly obtained fluxes, they were compared with already known frequency domain results for equatorial orbits and with results from a time domain Teukolsky equation solver called Teukode for off-equatorial orbits. The spinning body framework of our work is based on the Mathisson-Papapetrou-Dixon equations under the Tulczyjew-Dixon spin supplementary condition.

gr-qc↗

arXiv2023

Resonance crossing of a charged body in a magnetized Kerr background: an analogue of extreme mass ratio inspiral

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs.

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arXiv2022

Spinning test body orbiting around a Kerr black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits

The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon (MPD) equations when its centroid, i.e. its center of mass, is fixed by a Spin Supplementary Condition (SSC). In the present study, we continue the exploration of shifts between different centroids started in a recently published work [ Phys. Rev. D 104, 024042 (2021)], henceforth Paper I, for the Schwarzschild spacetime, by examining the frequencies of circular equatorial orbits under a change of the SSC in the Kerr spacetime. In particular, we examine the convergence in the terms of the prograde and retrograde orbital frequencies, when these frequencies are expanded in power series of the spin measure and the centroid of the body is shifted from the Mathisson-Pirani or the Ohashi-Kyrian-Semerak frame to the Tulczyjew-Dixon one. Since in Paper I, we have seen that the innermost stable circular orbits (ISCOs) hold a special place in this comparison process, we focus on them rigorously in this work. We introduce a novel method of finding ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the Mathisson-Pirani formalisms. We resort to numerical investigation of the convergence between the SSCs for the ISCO case, due to technical difficulties not allowing Paper's I analytical treatment. Our conclusion, as in Paper I, is that there appears to be a convergence in the power series of the frequencies between the SSCs, which is improved when the proper shifts are taken into account, but there exists a limit in this convergence due to the fact that in the spinning body approximation we consider only the first two lower multipoles of the extended body and ignore all the higher ones.

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