arXiv subjects

Zdeněk Stuchlík

Publications and source records attributed to Zdeněk Stuchlík.

At least 19 recordsLinked to original sources

arXiv2026

Timing of echoes in electromagnetic radiation from hot spots orbiting a Kerr black hole impostor

We investigate the light curve of an isolated bright spot in a Keplerian orbit around a Kerr black hole candidate to probe possible deviations from the standard event-horizon picture. In particular, we explore the presence of a reflective surface, namely a "mirror" near the horizon, and its observable consequences. We present estimates on the time delays of the echoes of electromagnetic radiation from the mirror or some other reflecting area related to black hole mimickers. Our results show that photon reflections from such a surface imprint distinct late-time features in the light curve, producing an electromagnetic analogue of gravitational wave echoes. For lower values of the spin, the reflected signal appears within the same orbital period and leads to a noticeable enhancement of the flux. In contrast, for higher spins, the effect emerges only after several orbits, giving rise to a characteristic echo-wave train. These features provide a potential observational signature of horizon-scale modifications in compact objects.

gr-qc↗

arXiv2026

Quasinormal Modes and Hawking Radiation of Black Holes with Primary Scalar Hair

Recently, a new family of asymptotically flat black-hole solutions endowed with primary scalar hair has been discovered in beyond-Horndeski gravity. We study in detail the quasinormal modes spectra, graybody factors, and Hawking radiation of this class of black holes. We demonstrate that presence of primary scalar hair leaves characteristic imprints on the ringdown properties, shifts the quasinormal frequencies, inducing overtone rearrangements, and rise of echoes. While the fundamental modes associated with the light-ring are affected moderately, higher overtones are highly sensitive to the small near-horizon deformation produced by scalar field. In certain parameter regimes, the graybody factors exhibit resonant-tunnelling behavior, which leads to an oscillatory frequency dependence of the Hawking emission rate. Thus, both black-hole spectroscopy and Hawking radiation may provide complementary and distinctive probes of the beyond-Horndeski gravity. Additionally, we demonstrate that the corresponding naked singularites are quantum mechanically singular and do not admit a well-defined dynamics.

gr-qc↗

arXiv2026

Shadows of naked singularities and superspinars related to the revisited Kerr-de Sitter spacetimes

We construct shadows of superspinars described by the revisited Kerr-de Sitter (rKdS) naked singularity (NS) spacetimes and compare them with those of the standard KdSNS spacetimes. For all the classes of the rKdSNS spacetimes we determine local escape cones related to variety of fundamental frames: locally nonrotating frames (LNRFs), radially escaping frames, and circular geodesic frames related to marginally stable obits of the rKdSNS spacetimes. The local escape cones (and their complementary cones) are then applied to construct the shadow of the KdS superspinars related to the distant static observers represented by the LNRFs located near the so-called static radius where the spacetime is close to the asymptotically flat region of the Kerr spacetimes, or the superspinars radially approaching, due to the Universe's expansion, the cosmic horizon of the spacetime. Differences of the shadows in the rKdSNS and standard KdSNS spacetimes are established and demonstrated for sufficiently large values of the dimensionless cosmological constant. For the observationally given cosmological constant and masses of the largest objects in the Universe, the shadow differences are not observable using recent observational instruments.

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arXiv2026

Observational signatures of misaligned double-ring and double-torus configurations around a Schwarzschild black hole

We investigate the observational signatures of an idealized double-ring and double-torus system orbiting a Schwarzschild black hole, allowing the two emitting components to have mutually inclined symmetry axes. Using general-relativistic ray tracing, we construct frequency-shift maps, bolometric flux maps on the observer's screen, and the corresponding spectral line profiles of the emitted radiation. The single equatorial torus is used as a reference configuration in order to isolate the effect of the second emitting component and of the mutual misalignment of the two structures. We show that the presence of two non-coplanar emitting structures produces characteristic multi-peak spectral profiles and asymmetric bolometric-flux distributions. These signatures are imprinted both in the line-profile morphology and in the $α$-profiles of the bolometric flux, providing simple diagnostic features of non-coplanar multi-component accretion structures.

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arXiv2026

Precision tests of analytical tail-term approximations for radiation reaction in Schwarzschild spacetime

We investigate the consistency and precision of approximate analytical expressions for the electromagnetic self-force acting on a charged particle in Schwarzschild spacetime endowed with weak electromagnetic fields. A fundamental requirement of relativistic particle dynamics is the preservation of the four-velocity normalization ($u^μu_μ=-1$), which implies that the total self-force must remain orthogonal to the particle's four-velocity. We introduce a covariant diagnostic based on the orthogonality condition ($u_μF^μ_{\text{tail}}=0$), which provides a quantitative measure of the internal consistency of approximate tail-term models used in radiation-reaction calculations. We apply this diagnostic to two widely used analytical approximations for the electromagnetic tail force: the conservative component derived by Smith and Will and the dissipative component derived by Gal'tsov. The analysis is performed for several physical configurations, including pure Schwarzschild spacetime, a weakly electrically charged Schwarzschild black hole, and a Schwarzschild black hole immersed in a weak external magnetic field. We find that the conservative Smith--Will term alone leads to small but measurable deviations from the orthogonality condition, while inclusion of the dissipative Gal'tsov contribution suppresses these deviations by many orders of magnitude. For realistic radiation-reaction parameters, the violation becomes extremely small. The proposed orthogonality diagnostic offers a simple and covariant tool for validating approximate self-force models in curved spacetime and may be useful for future studies of radiation-reaction dynamics near compact objects.

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arXiv2026

Electromagnetic radiation-reaction near black holes: orbital widening and the role of the tail

We investigate the orbital evolution of a classical charged particle around a Schwarzschild black hole immersed in an external, uniform magnetic field, taking into full account both local radiation-reaction and the nonlocal tail self-force arising in curved spacetime. Starting from the DeWitt-Brehme equation and its Landau-Lifshitz reduction, we derive analytic expressions for the conservative and dissipative components of the electromagnetic self-force in both the weak-field (Newtonian) and strong-field regimes. By implementing backward-in-time integration of the third-order DeWitt-Brehme equation alongside the second-order Landau-Lifshitz equation, we demonstrate that the so-called orbital widening effect persists even when the tail term is included, and that for astrophysically realistic charge-to-mass ratios the tail contribution to the trajectory is negligible. We further show that this widening is directly controlled by the product of the magnetic field and radiation-reaction parameters and can be captured in the Newtonian limit. Finally, we identify a scaling symmetry showing that simulations with moderate parameter values can accurately represent the dynamics in realistic astrophysical conditions, confirming that orbital widening is a robust phenomenon that can persist even in astrophysical black hole environments.

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arXiv2026

Dynamical and observational properties of weakly Proca-charged black holes

The simplest approach to include a mass into the electromagnetic vector potential is to modify the Einstein-Maxwell action to the Einstein-Proca form. There are currently no exact analytical solutions for this scenario. However, by using perturbation theory, where both the Proca mass and the black hole charge are small parameters, it is possible to find an exact analytical solution. In this solution, the metric tensor remains unchanged, but the vector potential deviates from the Coulomb potential. In particular, even if the Proca mass is limited by the value $m_γ<10^{-48}\text{g}$, which is the current experimental upper limit for photon mass, it makes a significant contribution to the dynamical equations. In this paper, we study the motion of neutral and charged particles in the vicinity of a weakly Proca-charged black hole, and test the observational implications of the solution of the Einstein-Proca equations for gravitational bending, the black hole shadow, and the fit to the orbits of the Galactic center flares observed by the near-infrared GRAVITY instrument. We find that only extremely cold photons, which are likely scattered before reaching a distant observer, could reveal the non-zero photon mass effect through the black hole shadow. For the Galactic center flare analysis we obtained constraints on the dimensionless Proca parameter to $μ\leq 0.125$ for the electric interaction parameter in the range $-1.1 < \mathrm{Q} < 0.5$, which can be potentially tested by future GRAVITY flare astrometry. Since the Proca parameter is coupled to the black hole mass, the effect of the Proca charge becomes more pronounced for supermassive black holes compared to stellar-mass objects. Our perturbative treatment remains valid essentially up to the horizon, with divergences appearing only in the immediate near-horizon region, where a fully non-perturbative analysis would be required.

gr-qc↗

arXiv2025

Stability of the rotating string loops in Kerr spacetime

We study stability of the circular string loops rotating in the equatorial plane of Kerr spacetime against equatorial and polar perturbations. We consider motion of such string loops for different modes in the case of arbitrary equation of state. We also obtain analytical expression for the fundamental frequencies of the string loop oscillations under equatorial and polar perturbations.

gr-qc↗

arXiv2025

Deterministic and Stochastic Study of the X-ray Emission from the TeV Blazar Mrk~421

We present a comprehensive timing analysis of X-ray data from the {\it XMM-Newton} satellite, examining 50 light curves covering 17 years of observations of the blazar Mrk~421. This work uses classical deterministic and stochastic methods in a novel way, enabling the distinction of temporal scales and offering essential insights through correlations among parameters. Deterministic behaviors are primarily explored through recurrence quantification analysis (RQA), used innovatively by varying the threshold input parameter to examine variability at multiple temporal scales. To investigate behavior across various scales from a stochastic perspective, we apply both autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models, with results from ARIMA more tightly related to short scales. Our findings reveal that Mrk~421's X-ray emission is a multifaceted process, driven by both deterministic and stochastic patterns, indicating a complex interplay of physical phenomena. Our study demonstrates that deterministic patterns are more pronounced at small temporal scales, which are disconnected from large scales. On the other hand, stochastic processes with memory propagate from large to small time scales, while noise affects both scales, as indicated by the correlation analysis. These results underscore the importance of advanced methodologies for interpreting astrophysical data, contributing to ongoing discussions in blazar physics by exploring connections between our calculated parameters and established models. The same approach can potentially be applied to other sources, enhancing our general understanding of variability and emission mechanisms in blazars.

astro-ph.HE↗

arXiv2025

Dark matter halos modeled by polytropic spheres influenced by the relict cosmological constant and trapping polytropes forming supermassive black holes

We study dark matter halos modeled by general relativistic polytropic spheres in spacetimes with the repulsive cosmological constant representing vacuum energy density, governed by a polytropic index $n$ and a relativistic (cosmological) parameter $σ$ ($λ$) determining the ratio of central pressure (vacuum energy density) and central energy density of the fluid. To give mapping of the polytrope parameters for matching extension and mass of large dark matter halos, we study properties of the polytropic spheres and introduce an effective potential of the geodesic motion in their internal spacetime. Circular geodesics enable us to find the limits of the trapping polytropes with central regions containing trapped null geodesics; supermassive black holes can be formed due to the instability of the central region against gravitational perturbations. Stability of the polytropic spheres relative to radial perturbations is determined. We match extension and mass of the polytropes to those of dark matter halos related to large galaxies or galaxy clusters, with extension $100 < \ell/\mathrm{kpc} < 5000$ and gravitational mass $10^{12} < M/M_\odot < 5 \times 10^{15}$. The observed velocity profiles simulated by the phenomenological dark matter halo density profiles can be well matched also by the velocity profiles of the exact polytrope spacetimes. The matching is possible by the non-relativistic polytropes for each value of $n$, with relativistic parameter $σ\leq 10^{-4}$ and very low central energy density. Surprisingly, the matching works for ``spread'' relativistic polytropes with $n > 3.3$ and $σ\geq 0.1$ when the central density can be much larger. The trapping polytropes forming supermassive black holes must have $n > 3.8$ and $σ> 0.667$.

gr-qc↗

arXiv2024

Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars

The motion of charged particles under the Lorentz force in the magnetosphere of neutron stars, represented by a dipole field in the Schwarzschild spacetime, can be determined by an effective potential, whose local extrema govern circular orbits both in and off the equatorial plane, which coincides with the symmetry plane of the dipole field. In this work, we provide a detailed description of the properties of these "conservative" circular orbits and, using the approximation represented by the Landau-Lifshitz equation, examine the role of the radiative back-reaction force that influences the motion of charged particles following both the in and off equatorial circular orbits, as well as the chaotic orbits confined to belts centered around the circular orbits. To provide clear insight into these dynamics, we compare particle motion with and without the back-reaction force. We demonstrate that, in the case of an attractive Lorentz force, the back-reaction leads to the charged particles falling onto the neutron star's surface in all scenarios considered. For the repulsive Lorentz force, in combination with the back-reaction force, we observe a widening of stable equatorial circular orbits; the off-equatorial orbits shift toward the equatorial plane and subsequently widen if they are sufficiently close to the plane. Otherwise, the off-equatorial orbits evolve toward the neutron star surface. The critical latitude, which separates orbital widening from falling onto the surface, is determined numerically as a function of the electromagnetic interaction's intensity.

astro-ph.HE↗

arXiv2024

Light escape cones in the locally non-rotating reference frames of the Kerr-de Sitter superspinars and related superspinar shadows

The construction of local escape cones and their complementary cones, related to the locally non-rotating frames (LNRFs) orbiting superspinars with the external field described by the Kerr-de Sitter (KdS) naked singularity (NS) spacetimes, is described for all possible classes of the KdS NS spacetimes and all possible positions of the photon emitter. The notion of the local escape cones is then applied to construct the shadow of the KdS superspinars related to the distant static observers represented by the LNRFs located near the so-called static radius where the spacetime is close to the asymptotically flat region of the Kerr spacetimes. The shadow construction is focused on the KdS superpsinars limited by the cosmological and astrophysical restrictions on the spacetime parameters, namely the superspinar dimensionless spin and the dimensionless cosmological parameter relating the cosmological constant and the superspinar's mass.

gr-qc↗

arXiv2024

Exploring a Novel Feature of Ellis Spacetime: Insights into Scalar Field Dynamics

We have studied neutral and charged massive particles dynamics in Ellis spacetime in the presence of the external scalar field. Focusing on the circular motion of massive particles, the impact of an external scalar field on the Innermost Stable Circular Orbit (ISCO) position is analyzed, revealing a non-linear relationship with the scalar field parameter. Perturbation techniques are employed to investigate oscillatory motion near stable orbits in the Ellis spacetime, yielding analytical expressions for radial and angular oscillations. The throat of the wormhole has been constrained by comparing theoretical and observational results for fundamental frequencies of particles from quasars. Finally, scalar and gravitational perturbations in the Ellis spacetime have been studied. It is shown that the equation for the scalar profile function is fully independent from the tensor functions, and the solution can be represented in terms of the confluent Heun function. However, it has been shown that equations for the tensor profile functions strongly depend on the scalar profile functions in the Ellis spacetime, and they are reduced to the Regge-Wheeler-Zerilli equation. Finally, numerical solutions to the Regge-Wheeler-Zerilli equation for the radial functions in the Ellis spacetime have been presented.

gr-qc↗

arXiv2024

Bridging Dimensions: General Embedding Algorithm and Field-Theory Reconstruction in 5D Braneworld Models

We develop a general algorithm that enables the consistent embedding of any four-dimensional static and spherically symmetric geometry into any five-dimensional single-brane braneworld model, characterized by an injective and nonsingular warp factor. Furthermore, we supplement the algorithm by introducing a method that allows one to, in principle, reconstruct 5D field theories that support the aforementioned geometries. This approach is based on a conformal transformation of the metric with the conformal factor being identified with the warp factor of the bulk geometry. The reconstructed theories depend solely on the induced brane geometry, since the warp factor is model-independently represented by a scalar field in the Lagrangian density. As a first application of our reconstruction method, we present for the first time a complete theory that supports the five-dimensional brane-localized extension of the Schwarzschild black hole, for any warp factor. The same method is subsequently utilized to illustrate the process of coherently embedding a de Sitter brane in braneworld models.

gr-qc↗

arXiv2024

Radiating particle in the vicinity of the weakly charged Schwarzschild black hole

It is well known that supermassive black holes in the centers of galaxies are capable of accelerating charged particles to very high energies. In many cases, the particle acceleration by black holes occurs electromagnetically through an electric field induced by the source. In such scenarios, the accelerated particles radiate electromagnetic waves, leading to the appearance of the backreaction force, which can considerably change the dynamics, especially, if the particles are relativistic. The effect of the radiation reaction force due to accelerating electric field of the central body in curved spacetime has not been considered previously. We study the dynamics of radiating charged particles in the field of the Schwarzschild black hole in the presence of an electric field associated with a small central charge of negligible gravitational influence. We start from the flat spacetime description, solving the Lorentz-Dirac equation reduced to the Landau-Lifshitz form. In curved spacetime, we use the DeWitt-Brehme equation and discuss the effect of the self-force, also known as the tail term, within the given approach. We also study the pure effect of the self-force to calculate the radiative deceleration of radially moving charged particles. In the case of bounded orbits, we find that the radiation reaction force can stabilize and circularize the orbits of oscillating charged particles by suppressing the oscillations or causing the particles to spiral down into the black hole depending on the sign of the electrostatic interaction. In all cases, we calculate the energy losses and exact trajectories of charged particles for different values and signs of electric charge.

gr-qc↗

arXiv2024

String loop vibration around Schwarzschild black hole

String loop vibrations in a central plane of a Schwarzschild black hole are investigated for various string equations of state. We discuss string loop stability and derive frequencies of vibrational modes. Using the vibrating string loop model we fit the quasi-periodic oscillation (QPO) observed in X-ray signal coming from some compact sources. We demonstrate how the string-loop parameters are related to the radial and vertical fundamental vibration modes, and how the vibrational instability can be related to the Q-factor characterizing the observed QPOs.

gr-qc↗

arXiv2023

Testing alternative spacetimes by high-frequency quasi-periodic oscillations observed in microquasars and active galactic nuclei

In this article, we try to capture the influence of deviation from standard Kerr black hole spacetime on observed high-frequency quasi-periodic oscillations signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr black hole spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency quasi-periodic oscillations data. We presented a generalized formalism for the fitting of the high-frequency quasi-periodic oscillations models so-called epicyclic resonance and relativistic precession models, under the assumption of stationary, axisymmetric, and asymptotically flat spacetimes. Recently, we have used the same set of stationary, axisymmetric, and asymptotically flat spacetimes, and estimated the restrictions of spacetime parameters with the help of hot-spot data of three flares observed at Sgr~A* by GRAVITY instrument \citep{Shahzadi-et-al:2022:EPJC:}. The aim of this work is not to test a particular theoretical model or to determine and constrain its parameters, but to map a set of well-astrophysically motivated deviations from classical Kerr black hole spacetime and demonstrate which ones provide the best fit for high-frequency quasi-periodic oscillations data and could be fruitful for future exploration.

gr-qc↗

arXiv2023

Spinning magnetized particles orbiting magnetized Schwarzschild black holes

A way to test electromagnetic field and spacetime properties around black holes is by considering the dynamics of test particles. In fact, in real astrophysical scenarios, it is hard to determine spacetime geometry which is dominating due to degeneracy gravitational effects in parameters of gravity theories. In this work, we study for the first time the dynamics of spinning particles that have magnetic dipole moments around Schwarzschild black holes immersed in an external asymptotically uniform magnetic field using the Mathisson-Papapetrou-Dixon (MPD) equation. There are two combined interactions: gravitational interaction between the spin of the particle and (electro)magnetic interaction between the external magnetic field and the magnetic dipole moment of the particle to be taken into account. First, we derive the effective potential of the test spinning magnetized particles in motion around the black hole. We also study the combined effects of spin and magnetic interactions on innermost stable circular orbits (ISCOs), the energy, and angular momentum of the particles at ISCO together with superluminal bounds. We investigated the collision of the particles and evaluated the center-of-mass energy in the collisions. Finally, we consider various cases in which neutron stars and rotating stellar mass black holes can be treated as spinning magnetized particles, evaluating the effects of the spin and magnetic moment of objects around supermassive and intermediate-mass black holes.

gr-qc↗