arXiv subjects

Zdeněk Stuchlík

Publications and source records attributed to Zdeněk Stuchlík.

At least 55 records · Page 3Linked to original sources

arXiv2021

Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes

Region of trapped null geodesics hidden inside of extremely compact objects is of astrophysical importance because of trapping of gravitational waves, or neutrinos. The trapping effect of null geodesics was extensively studied for spherically symmetric extremely compact objects. Recently, influence of rotation of the extremely compact objects on the trapping of null geodesics was treated in the simplest possible model of internal linearised \mbox{Hartle--Thorne} spacetime with uniform energy density distribution and uniform emissivity distribution of null geodesics. Here we extend the study of the rotation influence on the trapping effect in the case of linearized \mbox{Hartle--Thorne} spacetimes based on the Tolman VII spherically symmetric solutions, where we assume the emissivity of the null geodesics proportional to the energy density of the Tolman VII object having quadratic radial profile. We demonstrate enhancement (suppression) of the trapping effect in the case of counter-rotating (co-rotating) null geodesics due to the behavior of the effective potentials and escape cones of the null geodesics in the linearised Hartle--Thorne--Tolman VII spacetimes. In dependence on the parameters of these spacetimes we determine the "local" and "global" coefficients of efficiency of the trapping and compare the results to those related to the rotating spacetimes based on the internal Schwarzschild spacetimes. We demonstrate that in the Tolman VII spacetimes the trapping is more efficient, being allowed in objects with radii larger than those of the trapping internal Schwarzschild spacetimes, occurring even for $R>3.3M$.

gr-qc↗

arXiv2021

Epicyclic Oscillations around Simpson-Visser Regular Black Holes and Wormholes

We study epicyclic oscillatory motion along circular geodesics of the Simpson--Visser meta-geometry describing in a unique way regular black-bounce black holes and reflection-symmetric wormholes by using a length parameter $l$. We give the frequencies of the orbital and epicyclic motion in a Keplerian disc with inner edge at the innermost circular geodesic located above the black hole outer horizon or on the our side of the wormhole. We use these frequencies in the epicyclic resonance version of the so-called geodesic models of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars and around supermassive black holes in active galactic nuclei to test the ability of this meta-geometry to improve the fitting of HF QPOs observational data from the surrounding of supermassive black holes. We demonstrate that this is really possible for wormholes with sufficiently high length parameter $l$.

gr-qc↗

arXiv2021

Neutrino trapping in extremely compact Tolman VII spacetimes

Extremely compact objects trap gravitational waves or neutrinos, assumed to move along null geodesics in the trapping regions. The trapping of neutrinos was extensively studied for spherically symmetric extremely compact objects constructed under the simplest approximation of the uniform energy density distribution, with radius located under the photosphere of the external spacetime; in addition, uniform emissivity distribution of neutrinos was assumed in these studies. Here we extend the studies of the neutrino trapping for the case of the extremely compact Tolman VII objects representing the simplest generalization of the internal Schwarzschild solution with uniform distribution of the energy density, and the correspondingly related distribution of the neutrino emissivity that is thus again proportional to the energy density; radius of such extremely compact objects can overcome the photosphere of the external Schwarzschild spacetime. In dependence on the parameters of the Tolman VII spacetimes, we determine the "local" and "global" coefficients of efficiency of the trapping and demonstrate that the role of the trapping is significantly stronger than in the internal Schwarzschild spacetimes. Our results indicate possible influence of the neutrino trapping in cooling of neutron stars.

gr-qc↗

arXiv2021

Dynamical stability of the modified Tolman VII solution

Studies of neutron stars are at their peak after the multi-messenger observation of the binary merger event GW170817, which strongly constraints the stellar parameters like tidal deformability, masses and radii. Although current and future observations will provide stronger limits on the neutron stars parameters, knowledge of explicit interior solutions to Einstein's equations, which connect observed parameters with the internal structure, are crucial to have a satisfactory description of the interior of these compact objects. A well known exact solution, which has shown a relatively good approximation to a neutron star, is the Tolman VII solution. In order to provide a better fitting for the energy density profile, with the realistic equations of state for neutron stars, recently Jiang and Yagi proposed a modified version of this model which introduces an additional parameter $α$ reflecting the interplay of the quadratic and the newly added quartic term in the energy density profile. Here we study the dynamical stability of this modified Tolman VII solution using the theory of infinitesimal and adiabatic radial oscillations developed by Chandrasekhar. For this purpose, we determine values of the critical adiabatic index, for the onset of instability, considering configurations with varying compactness and $α$. We found that the new models are stable against radial oscillations for a considerable range of values of compactness and the new parameter $α$, thus supporting their applicability as a physically plausible approximation of realistic neutron stars.

gr-qc↗

arXiv2021

Epicyclic oscillations in spinning particle motion around Kerr black hole applied in models fitting the quasi-periodic oscillations observed in quasars and microquasars

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries or quasars can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus fit the data of QPOs observed in the well known quasars as well as microquasars in the framework of the model of geodesic oscillations of Keplerian disks modified for the epicyclic oscillations of spinning test particles orbiting Kerr BHs. We show that the modified geodesic models of QPOs can explain the observational fixed data from the quasars and microquasars but not for all sources. We perform a successful fitting of the high frequency QPOs models of epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, and discuss the corresponding constraints of parameters of the model, which are the spin $S$ of the test particle, mass $M$ and spin $a$ of the BH.

astro-ph.HE↗

arXiv2021

Polytropic spheres modelling dark matter halos of dwarf galaxies

Dwarf galaxies and their dark matter (DM) halos have the velocity curves of a different character than those in large galaxies. They are modelled by a simple pseudo iso-thermal model containing only two parameters that do not allow to obtain insight into physics of the DM halo. We would like to obtain some insight into the physical conditions in DM halos of dwarf galaxies by using a simple physically based model of DM halos. In order to treat a diversity of the dwarf galaxy velocity profiles in a unifying framework, we apply the polytropic spheres characterised by the polytropic index $n$ and the relativistic parameter $σ$ as a model of dwarf-galaxy DM halos and match the velocity of circular geodesics of the polytropes to the velocity curves observed in the dwarf galaxies from the LITTLE THINGS ensemble. We introduce three classes of the LITTLE THINGS dwarf galaxies in accord with the polytrope models, due to the different character of the velocity profile. The first class corresponds to polytropes having $n < 1$ with linearly increasing velocity along with the whole profile, the second class has $1 < n < 2$ and the velocity profile becomes flat in the external region, the third class has $n > 2$ and the velocity profile reaches a maximum and demonstrated a decline in the external region. The $σ$ parameter has to be strongly non-relativistic ($σ< 10^{-8}$) for all dwarf galaxy models -- it varies for the models of each class, but these variations have a negligible influence on the character of the velocity profile. Our results indicate the possibility that at least two different kinds of dark matter are behind the composition of DM halos. The matches of the observational velocity curves are of the same quality as those obtained by the pseudo-isothermal, core-like models of dwarf galaxy DM halos.

astro-ph.CO↗

arXiv2020

Detection of chaotic behavior in time series

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there originating time series. Chaos in time series resembles stochastic behavior, but apart of randomness it is totally deterministic and therefore chaotic data can provide us useful information. Therefore it is essential to have methods, which are able to detect chaos in time series, moreover to distinguish chaotic data from stochastic one. Here we present and discuss the performance of standard and machine learning methods for chaos detection and its implementation on two well known simple chaotic discrete dynamical systems - Logistic map and Tent map, which fit to the most of the definitions of chaos.

physics.comp-ph↗

arXiv2020

Charged fluids encircling compact objects: force representations and conformal geometries

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy-momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy-momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

gr-qc↗

arXiv2020

Trapping of null geodesics in slowly rotating spacetimes

Extremely compact objects containing a region of trapped null geodesics could be of astrophysical relevance due to trapping of neutrinos with consequent impact on cooling processes or trapping of gravitational waves. These objects have previously been studied under the assumption of spherical symmetry. In the present paper, we consider a simple generalization by studying trapping of null geodesics in the framework of the Hartle-Thorne slow-rotation approximation taken to first order in the angular velocity, and considering a uniform-density object with uniform emissivity for the null geodesics. We calculate effective potentials and escape cones for the null geodesics and how they depend on the parameters of the spacetimes, and also calculate the "local" and "global" coefficients of efficiency for the trapping. We demonstrate that due to the rotation the trapping efficiency is different for co-rotating and retrograde null geodesics, and that trapping can occur even for $R>3GM/c^2$, contrary to what happens in the absence of rotation.

gr-qc↗

arXiv2020

Deterministic Aspect of the $γ$-ray Variability in Blazars

Linear time series analysis, mainly the Fourier transform based methods, has been quite successful in extracting information contained in the ever-modulating light curves (Lcs) of active galactic nuclei, and thereby contribute in characterizing the general features of supermassive black hole systems. In particular, the statistical properties of $γ$-ray variability of blazars are found to be fairly represented by flicker noise in the temporal frequency domain. However, these conventional methods have not been able to fully encapsulate the richness and the complexity displayed in the light curves of the sources. In this work, to complement our previous study on the similar topic, we perform non-linear time series analysis of the decade-long Fermi/LAT observations of 20 $γ$-ray bright blazars. The study is motivated to address one of the most relevant queries that whether the dominant dynamical processes leading to the observed $γ$-ray variability are of deterministic or stochastic nature. For the purpose, we perform Recurrence Quantification Analysis of the blazars and directly measure the quantities which suggest that the dynamical processes in blazar could be a combination of deterministic and stochastic processes, while some of the source light curves revealed significant deterministic content. The result with possible implication of strong disk-jet connection in blazars could prove to be significantly useful in constructing models that can explain the rich and complex multi-wavelength observational features in active galactic nuclei. In addition, we estimate the dynamical timescales, so called "trapping timescales", in the order of a few weeks.

astro-ph.HE↗

arXiv2020

Radiative Penrose process: Energy Gain by a Single Radiating Charged Particle in the Ergosphere of Rotating Black Hole

We demonstrate an extraordinary effect of energy gain by a single radiating charged particle inside the ergosphere of a Kerr black hole in presence of magnetic field. We solve numerically the covariant form of the Lorentz-Dirac equation reduced from the DeWitt-Brehme equation and analyze energy evolution of the radiating charged particle inside the ergosphere, where the energy of emitted radiation can be negative with respect to a distant observer in dependence on the relative orientation of the magnetic field, black hole spin and the direction of the charged particle motion. Consequently, the charged particle can leave the ergosphere with energy greater than initial in expense of black hole's rotational energy. In contrast to the original Penrose process and its various modification, the new process does not require the interactions (collisions or decay) with other particles and consequent restrictions on the relative velocities between fragments. We show that such a Radiative Penrose effect is potentially observable and discuss its possible relevance in formation of relativistic jets and in similar high-energy astrophysical settings.

gr-qc↗

arXiv2020

Test particle motion around black hole in Einstein-Maxwell-scalar theory

In this paper, we explore the test particle motion around a black hole in Einstein-Maxwell-scalar (EMS) theory using three different black hole solutions within this theory. We have first analyzed the spacetime curvature structure of these solutions and shown the existence of two singularities and the first one is at the center $r=0$. In black hole spacetime, there are two regions divided by the critical value of the cosmological parameter $λ_0$. The photon sphere around the black hole in EMS theory has also been studied and found that it does not depend on cosmological parameter $λ$. We have analyzed the innermost stable circular orbits (ISCO) around the black hole and shown that for all solutions ISCO radius for neutral particle decreases with the increase of black hole charge. We have also studied the charged particle motion around the black hole where charged particle motion is considered in the presence of the gravitational field and the Coulomb potential. It is shown that ISCO radius for charged particles increases depending on the selected value of the coupling parameter which is in contradiction with observations of the inner edge of the accretion disks of the astrophysical black holes and can be used as a powerful tool to rule out the EMS theory from consideration for the gravitational field theory. It is also studied the fundamental frequencies governed by test particle orbiting around the black hole in EMS theory. Finally, as a test of black hole solution in EMS theory ISCO radii is compared with that in Kerr black hole and found that the spin parameter of Kerr can be mimic up to $a/M\simeq 0.936$.

gr-qc↗

arXiv2020

Charged particle and epicyclic motions around $4D$ Einstein-Gauss-Bonnet black hole immersed in an external magnetic field

We investigate particle motion in the vicinity of a $4D$ Einstein-Gauss-Bonnet (EGB) black hole immersed in external asymptotically uniform magnetic field. It is well known that magnetic fields can strongly affect charged particle motion in the black hole vicinity due to the Lorenz force. We find that the presence of the Gauss-Bonnet (GB) coupling gives rise to a similar effect, reducing the radius of the innermost stable circular orbit (ISCO) with respect to the purely relativistic Schwarzschild black hole. Further, we consider particle collisions in the black hole vicinity to determine the center of mass energy and show that this energy increases with respect to the Schwarzschild case due to the effect of the GB term. Finally, we consider epicyclic motion and its frequencies and resonance as a mean to test the predictions of the model against astrophysical observations. In particular we test which values of the parameters of the theory best fit the 3:2 resonance of high-frequency quasi-periodic oscillations in three low-mass X-ray binaries.

gr-qc↗

arXiv2020

Effect of Electromagnetic Interaction on Galactic Center Flare Components

Recently, near-infrared GRAVITY@ESO observations at $2.2\,μ{\rm m}$ have announced the detection of three bright "flares" in the vicinity of the Galactic center supermassive black hole (SMBH) that exhibited orbital motion at a distance of about $6 - 11$ gravitational radii from an $\sim 4\times 10^6\, M_{\odot}$ black hole. There are indications of the presence of a large-scale, organized component of the magnetic field at the Galactic center. Electromagnetic effects on the flare dynamics were previously not taken into account despite the relativistic motion of a plasma in magnetic field leading to the charge separation and nonnegligible net charge density in the plasma. Applying various approaches, we find the net charge number density of the flare components of the order of $10^{-3} - 10^{-4}$ cm$^{-3}$, while the particles' total number density is of the order of $10^{6} - 10^{8}$ cm$^{-3}$. However, even such a tiny excess of charged particles in the quasi-neutral plasma can significantly affect the dynamics of flare components, which can then lead to the degeneracy in the measurements of spin of the SMBH. Analyzing the dynamics of recent flares in the case of the rapidly rotating black hole, we also constrain the inclination angle between the magnetic field and spin axis to $α< 50^{\circ}$, as for larger angles, the motion of the hot spot is strongly chaotic.

astro-ph.GA↗

arXiv2020

Supermassive black holes as possible sources of ultra high energy cosmic rays

Production and acceleration mechanisms of ultra-high-energy cosmic rays (UHECRs) of energy $>10^{20}$eV, clearly beyond the GZK-cutoff limit remain unclear that points to exotic nature of the phenomena. Recent observations of extragalactic neutrino may indicate the source of UHECRs being an extragalactic supermassive black hole (SMBH). We demonstrate that ultra-efficient energy extraction from rotating SMBH driven by the magnetic Penrose process (MPP) could indeed foot the bill. We envision ionization of neutral particles, such as neutron beta-decay, skirting close to the black hole horizon that energizes protons to over $10^{20}$eV for SMBH of mass $10^9 M_{\odot}$ and magnetic field of strength $10^4$G. Applied to Galactic center SMBH we have proton energy of order $\approx 10^{15.6}$eV that coincides with the knee of the cosmic ray spectra. We show that large $γ_z$ factors of high-energy particles along the escaping directions occur only in the presence of induced charge of the black hole that is known as the Wald charge in the case of uniform magnetic field. It is remarkable that the process neither requires extended acceleration zone, nor fine-tuning of accreting matter parameters. Further, this leads to certain verifiable constraints on SMBH's mass and magnetic field strength as UHECRs sources. This clearly makes ultra-efficient regime of MPP one of the most promising mechanisms for fueling UHECRs powerhouse.

astro-ph.HE↗

arXiv2020

Radial instability of trapping polytropic spheres

We complete the stability study of general relativistic spherically symmetric polytropic perfect fluid spheres, concentrating attention to the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm-Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5, and the relativistic parameter σ given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter σ. For the dynamical approach we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of σ. We found that all the configurations having trapped null geodesics are unstable according to both methods.

gr-qc↗

arXiv2019

Particle motion around generic black holes coupled to non-linear electrodynamics

We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.

gr-qc↗

arXiv2019

Anisotropic Tolman VII solution by gravitational decoupling

Using the gravitational decoupling by the minimal geometric deformation approach, we build an anisotropic version of the well-known Tolman VII solution, determining an exact and physically acceptable interior two-fluid solution that can represent behavior of compact objects. Comparison of the effective density and density of the perfect fluid is demonstrated explicitly. We show that the radial and tangential pressure are different in magnitude giving thus the anisotropy of the modified Tolman VII solution. The dependence of the anisotropy on the coupling constant is also shown.

gr-qc↗