arXiv subjects

Vojtěch Witzany

Publications and source records attributed to Vojtěch Witzany.

At least 19 recordsLinked to original sources

arXiv2026

Multimessenger prospects of quasi-periodic eruptions

Quasi-Periodic Eruptions (QPEs) are recurring soft X-ray transients that may be generated by inspirals of stellar-mass objects spiraling into supermassive black holes, known as extreme mass ratio inspirals (EMRIs). Independently, EMRIs and the gravitational-wave signals they generate are one of the key targets for the Laser Interferometer Space Antenna (LISA). What is the potential of a coincident detection of EMRIs both as a QPE and by LISA? Electromagnetic counterparts to LISA events would provide sky localization, enable standard siren measurements of the Hubble constant and constrain formation mechanisms of the corresponding inspirals. Combined observations would link the accurate measurements of black hole masses and spins to their galactic nuclear environments and would thus enable lasting synergies with various observations across the electromagnetic spectrum. However, most of the currently known QPEs imply EMRI orbital periods that place the frequencies of the corresponding gravitational-wave signal out of the LISA sensitivity band. Additionally, the selection biases of QPE detections and the LISA instrument may preclude a coincident detection. Future searches should focus on expanding the QPE catalogs and ultimately hunt for ``golden'' short-period QPEs that correspond to EMRIs that fall within the LISA band.

astro-ph.HE↗

arXiv2026

Separability of the motion of spinning test particles in curved space-time

Solving for the motion of spinning test particles in curved spacetimes is important for modeling gravitational-wave inspirals of spinning compact binaries. We build a Hamiltonian formalism in worldline-adapted tetrads for the spinning test particle and formulate a corresponding Hamilton-Jacobi equation valid to linear order in spin. We prove that when the geodesic motion in a spacetime and the parallel transport along said geodesics are both separable, then so is the corresponding Hamilton-Jacobi equation. We illustrate this in black hole, plane wave, and cosmological spacetimes.

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arXiv2025

Toward relativistic inspirals into black holes surrounded by matter

Extreme mass ratio inspirals, compact objects spiraling into massive black holes, represent key sources for future space-based gravitational-wave detectors such as LISA. The inspirals will occur within rich astrophysical environments containing gravitating matter. Motivated by this, we develop a fully relativistic framework for inspirals under the gravitational influence of matter environments. Our approach employs a two-parameter perturbation expansion in the mass ratio and an environmental parameter. This yields a modified Teukolsky equation capturing the leading cross-order. We then implement a simple pole-dipole approximation of an axisymmetric environment through a thin matter shell and restrict to non-rotating black holes. As a result, we obtain a piecewise type D spacetime. This enables the use of Teukolsky-based methods while accounting for junction physics. The presence of the matter shell leads to effectively non-separable boundary conditions for the Teukolsky scalar and introduces mode mixing between adjacent multipoles. Additionally, the shell oscillates under the wave perturbation of the inspiral, contributing to the overall flux. The framework provides novel insights into the global dynamics of gravitational radiation in tidal environments. Furthermore, it represents a complete theoretical foundation for a future computation of inspirals and waveforms in our environmental model.

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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

Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time

The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show that separability of the equations of motion can be recovered to linear order in spin by a shift of the worldline derived with the use of the hidden symmetry of Kerr space-time. Consequently, the closed-form solution of the motion is expressed in a way closely analogous to the solution for spinless particles. This finding enriches the understanding of separability and integrability properties of the dynamics of test particles and fields in Kerr space-time and is particularly valuable for modeling inspirals of rotating compact objects into massive black holes.

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arXiv2025

Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits.

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arXiv2024

Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes

Space-based gravitational-wave detectors such as LISA are expected to detect inspirals of stellar-mass compact objects into massive black holes. Modeling such inspirals requires fully relativistic computations to achieve sufficient accuracy at leading order. However, subleading corrections such as the effects of the spin of the inspiraling compact object may potentially be treated in weak-field expansions such as the post-Newtonian (PN) approach. In this work, we calculate the PN expansion of eccentric orbits of spinning bodies around Schwarzschild black holes. Then we use the Teukolsky equation to compute the energy and angular momentum fluxes from these orbits up to the 5PN order. Some of these PN orders are exact in eccentricity, while others are expanded up to the tenth power in eccentricity. Then we use the fluxes to construct a hybrid inspiral model, where the leading part of the fluxes is calculated numerically in the fully relativistic regime, while the linear part in the small spin is analytically approximated using the PN series. We calculate LISA-relevant adiabatic inspirals and respective waveforms with this model and a fully relativistic model. Through the calculation of mismatch between the waveforms from both models we conclude that the PN approximation of the linear-in-spin part of the fluxes is sufficient for lower eccentricities.

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arXiv2024

Alive and Strongly Kicking: Stable X-ray Quasi-Periodic Eruptions from eRO-QPE2 over 3.5 Years

Quasi-periodic eruptions (QPEs) are recurring bursts of soft X-rays from the nuclei of galaxies. Their physical origin is currently a subject of debate, with models typically invoking an orbiter around a massive black hole or disk instabilities. Here we present and analyze the temporal and spectral evolution of the QPE source eRO-QPE2 over 3.5 years. We find that eRO-QPE2 1) is remarkably stable over the entire 3.5-year temporal baseline in its eruption peak luminosity, eruption temperature, quiescent temperature, and quiescent luminosity, 2) has a stable mean eruption recurrence time of 2.35 hours, with marginal ($\sim$2$σ$) evidence for a $0.1$ hour reduction over the 3.5 yr period, and 3) has a long-short variation in its recurrence time in August 2020, but this pattern is absent from all subsequent observations. The stability of its peak eruption luminosity and that of the quiescent state are notably dissimilar from three previously tracked QPEs (GSN069, eRO-QPE1, eRO-QPE3), which show declines in eruption and quiescent flux over comparable temporal baselines. This stability is even more pronounced in eRO-QPE2 due to its 2.4 hour average recurrence time compared to GSN-069's 9 hour, eRO-QPE1's 16 hour, and eRO-QPE3's 20 hour recurrence times, i.e., this system has undergone 4-8 times more cycles than these other systems over the 3.5 years of observations. We discuss the implications of these observations within the context of some proposed extreme mass ratio inspiral (EMRI) models.

astro-ph.HE↗

arXiv2024

Fast inspirals and the treatment of orbital resonances

Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ($ε\sim 10^{-4}$--$10^{-7}$), the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute. In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called "resonant phase". Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from $\mathcal{O}(ε^{-1/2})$ in the fully averaged scheme to $\mathcal{O}(ε^{4/7})$ in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to $ε$ using OG, to a very weak scaling with $ε$. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation.

gr-qc↗

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.

gr-qc↗

arXiv2024

X-ray eruptions every 22 days from the nucleus of a nearby galaxy

Galactic nuclei showing recurrent phases of activity and quiescence have recently been discovered, with recurrence times as short as a few hours to a day -- known as quasi-periodic X-ray eruption (QPE) sources -- to as long as hundreds to a thousand days for repeating nuclear transients (RNTs). Here we present a multi-wavelength overview of Swift J023017.0+283603 (hereafter Swift J0230+28), a source that exhibits repeating and quasi-periodic X-ray flares from the nucleus of a previously unremarkable galaxy at $\sim$ 165 Mpc, with a recurrence time of approximately 22 days, an intermediary timescale between known RNTs and QPE sources. The source also shows transient radio emission, likely associated with the X-ray emission. Such recurrent soft X-ray eruptions, with no accompanying UV/optical emission, are strikingly similar to QPE sources. However, in addition to having a recurrence time that is $\sim 25$ times longer than the longest-known QPE source, Swift J0230+28's eruptions exhibit somewhat distinct shapes and temperature evolution than the known QPE sources. Scenarios involving extreme mass ratio inspirals are favored over disk instability models. The source reveals an unexplored timescale for repeating extragalactic transients and highlights the need for a wide-field, time-domain X-ray mission to explore the parameter space of recurring X-ray transients.

astro-ph.HE↗

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↗

arXiv2022

Action-angle coordinates for black-hole geodesics I: Spherically symmetric and Schwarzschild

Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for bound test particle motion in static, spherically symmetric space-times using a post-circular expansion. Then I specialise the expressions to the motion in the gravitational fields of Schwarzschild black holes and give explicit formulas for the Hamiltonian to the 10th power in the radial action (20th power in eccentricity), and the transformation to angle coordinates up to the 8th harmonic with respect to a relativistic orbital anomaly. The results provide a closed-form perturbative solution for the orbital motion parametrized by coordinate time that will find applications in the modelling of compact binary inspirals and other fields of astrophysics.

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arXiv2021

Einstein gravity as a theory with a SL(2,C) connection double copy

Results ranging from Ashtekar variables to the perturbative Bern-Carrasco-Johansson (BCJ) double copy suggest a deep relation between Yang-Mills theory and Einstein gravity. I examine this relation by writing down the tetradic Palatini action for Einstein gravity and covariantly decomposing its variables into two $SL(2,\mathbb{C})$ connections and two soldering forms. This leads to a conjecture that the BCJ double copy can be understood through a "holomorphic trail", a series of injection maps between two copies of $SU(2)$ theories and Einstein gravity.

gr-qc↗

arXiv2021

Stellar transits across a magnetized accretion torus as a mechanism for plasmoid ejection

The close neighbourhood of a supermassive black hole contains not only the accreting gas and dust but also stellar-sized objects, such as late-type and early-type stars and compact remnants that belong to the nuclear star cluster. When passing through the accretion flow, these objects perturb it by the direct action of stellar winds, as well as their magnetic and gravitational effects. By performing General-Relativistic Magnetohydrodynamic (GRMHD) simulations, we investigate how the passages of a star can influence the supermassive black hole gaseous environment. We focus on the changes in the accretion rate and the emergence of blobs of plasma in the funnel of an accretion torus. We compare results from 2D and 3D numerical computations that have been started with comparable initial conditions. We find that a quasi-stationary inflow can be temporarily inhibited by a transiting star, and the plasmoids can be ejected along the magnetic field lines near the rotation axis. We observe the characteristic signatures of the perturbing motion in the power spectrum of the accretion variability, which provides an avenue for a multi-messenger detection of these transient events. Finally, we discuss the connection of our results to multi-wavelength observations of galactic nuclei, with the emphasis on ten promising sources (Sgr~A*, OJ 287, J0849$+$5108, RE J1034$+$396, 1ES 1927+65, ESO 253--G003, GSN 069, RX J1301.9$+$2747, eRO-QPE1, eRO-QPE2).

astro-ph.HE↗

arXiv2021

Non-linear effects in EMRI dynamics and their imprints on gravitational waves

The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this conservative system is smooth and there are no "topological transitions" in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral. However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play. In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model. Even though many of the developments of this chapter apply to general inspirals, we focus on a particular scenario known as the Extreme mass ratio inspiral (EMRI). An EMRI consists of a compact stellar-mass object inspiralling into a supermassive black hole. At leading order, the referential conservative system is simply geodesic motion in the field of the supermassive black hole and the rate of the drift is given by radiation reaction. In Einstein gravity the supermassive black hole field is the Kerr space-time in which the geodesic motion is integrable. However, the equations of motion can be perturbed in various ways so that prolonged resonances and chaos appear in phase space as well as the inspiral, which we demonstrate in simple physically motivated examples.

gr-qc↗

arXiv2020

Perturbing the accretion flow onto a supermassive black hole by a passing star

The close neighbourhood of a supermassive black hole contains not only accreting gas and dust, but also stellar-sized objects like stars, stellar-mass black holes, neutron stars, and dust-enshrouded objects that altogether form a dense nuclear star-cluster. These objects interact with the accreting medium and they perturb the otherwise quasi-stationary configuration of the accretion flow. We investigate how the passages of a star can influence the black hole gaseous environment with GRMHD 2D and 3D simulations. We focus on the changes in the accretion rate and the associated emergence of outflowing blobs of plasma.

astro-ph.HE↗