A charged particle kicked from an initial circular orbit around a weakly magnetized Schwarzschild black hole undergoes transient chaotic motion before either getting captured by the black hole or escaping upstream or downstream with respect to the direction of the magnetic field. These final states form basins of attraction in the space of initial states. We provide a detailed numerical study of the basin structure of this initial state space. We find it to possess the peculiar Wada property: each of its basin boundaries is shared by all three basins. Using basin entropy as a measure, we show that uncertainty in predicting the final exit state increases with stronger magnetic interaction. We also present an approximate analytic expression of the critical escape energy for a vertically-kicked charged particle, and discuss how this depends on the strength of the magnetic interaction.
Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry. Embedding diagrams are constructed in order to visualize the geometry of the metric. The study performed here is also valid, when the electromagnetic interactions are neglected, for the low energy superstring theory and the Brans-Dicke theory.
Neutral test particles around a Schwarzschild black hole immersed in an external uniform magnetic field have no interactions of electromagnetic forces, but their motions can be chaotic. This chaotic behavior is induced owing to the gravitational effect of the magnetic field leading to the nonintegrability of the magnetized Ernst-Schwarzschild spacetime geometry. In fact, chaos is strengthened typically with an increase of the energy or the magnetic field under appropriate circumstances. When these test particles have charges, the electromagnetic forces are included. As a result, the electromag…
We study the circular orbits of charged particles around a weakly charged Schwarzschild black hole immersed in a weak, axisymmetric magnetic field. We start by reviewing the circular orbits of neutral particles and charged particles around only weakly charged and only weakly magnetized black holes. The case of a weakly magnetized and charged black hole is investigated then. In particular, we study the effect of the electromagnetic forces on the charged particles innermost stable circular orbits. We show that negative energy stable circular orbits are possible and that two bands of charged part…
Comments on Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit, arXiv:2406.03371v2
In this paper, we have presented the studies of the motion of magnetized particles and energetic processes around Schwarzschild black holes in modified gravity (MOG). The study of circular stable orbits shows that orbits of magnetized particles can not be stable for the values of magnetic coupling parameter $β\geq 1$. It was also shown that the range of stable circular orbits increases with the increase of both MOG and magnetic coupling parameters, while the effects of magnetic interaction stronger than the gravity. It was obtained that the increase of the MOG parameter causes the increase of …
We consider a synchrotron radiation from a charged particle moving in a bound orbit around a weakly magnetized Schwarzschild black hole (a static black hole immersed into a constant uniform magnetic field) in its equatorial plane, perpendicular to the magnetic field. In particular, we study the case when the Lorentz force acting on the charged particle is directed outward from the black hole. The particle is initially moving in a nongeodesic bound orbit which due to synchrotron radiation decays to a nongeodesic circular orbit. We study this transition and calculate the radiated power and energ…
This paper investigates wave properties of hot plasma in a Veselago medium. For the Schwarzschild black hole, the $3+1$ GRMHD equations are re-formulated which are linearly perturbed and then Fourier analyzed for rotating (non-magnetized and magnetized) plasmas. The graphs of wave vector, refractive index and change in refractive are used to discuss the wave properties. The results obtained confirm the presence of Veselago medium for both rotating (non-magnetized and magnetized) plasmas. This work generalized the isothermal plasma waves in the Veselago medium to hot plasma case.
We re-formulate the 3+1 GRMHD equations for the Schwarzschild black hole in a Veselago medium. Linear perturbation in rotating (non-magnetized and magnetized) plasma is introduced and their Fourier analysis is considered. We discuss wave properties with the help of wave vector, refractive index and change in refractive index in the form of graphs. It is concluded that some waves move away from the event horizon in this unusual medium. We conclude that for the rotating non-magnetized plasma, our results confirm the presence of Veselago medium while the rotating magnetized plasma does not provid…
We discuss charged particles motion in a spacetime of a weakly magnetized static non-rotating black hole. We study under which conditions a charged particle originally revolving around the black hole at a circular orbit after being kicked by another particle or photon can escape to infinity. We determine the escape velocity for particles at the innermost stable circular orbits and discuss the properties of particles moving with near-critical velocity. We show that in a general case such a motion is chaotic.
In this paper, we study the influence of the axion-plasmon, as proposed in (Phys. Rev. Lett. 120, 181803 (2018)) on the optical properties of the Schwarzschild black hole. Our aim is to provide a test to detect the effects of a fixed axion background using black holes. To accomplish our goal, we explore the effect of the axion-plasmon coupling on the motion of photons around the Schwarzschild black hole and check the possibility of observing those effects upon the black hole shadow, the gravitational deflection angle, Einstein rings and shadow images obtained by radially infalling gas on a bla…
We study motion of a charged particle in the vicinity of a weakly magnetized Schwarzschild black hole and focus on its bounded trajectories lying in the black hole equatorial plane. If the Lorentz force, acting on the particle, is directed outward from the black hole, there exist two qualitatively different types of trajectories, one is a curly motion and another one is a trajectory without curls. We calculated the critical value of the magnetic field for the transition between these two types. If the magnetic field is greater than the critical one, for fixed values of the particle energy and …
In this paper we consider magnetized black holes and black rings in the higher dimensional dilaton gravity. Our study is based on exact solutions generated by applying a Harrison transformation to known asymptotically flat black hole and black ring solutions in higher dimensional spacetimes. The explicit solutions include the magnetized version of the higher dimensional Schwarzschild-Tangherlini black holes, Myers-Perry black holes and five dimensional (dipole) black rings. The basic physical quantities of the magnetized objects are calculated. We also discuss some properties of the solutions …
It has recently been demonstrated that magnetized black holes in composed Einstein-Maxwell-scalar-Gauss-Bonnet field theories with a non-minimal negative coupling of the scalar field to the Gauss-Bonnet curvature invariant may support spatially regular scalar hairy configurations. In particular, it has been revealed that, for Schwarzschild-Melvin black-hole spacetimes, the onset of the near-horizon spontaneous scalarization phenomenon is marked by the numerically computed dimensionless critical relation $(BM)_{\text{crit}}\simeq0.971$, where $\{M,B\}$ are respectively the mass and the magnetic…
In this paper we examine the wave properties of hot plasma living in Schwarzschild magnetosphere. The 3+1 GRMHD perturbation equations are formulated for this scenario. These equations are Fourier analyzed and then solved numerically to obtain the dispersion relations for non-rotating, rotating non-magnetized and rotating magnetized plasma. The wave vector is evaluated which is used to calculate refractive index. These quantities are shown in graphs which are helpful to discuss the dispersive properties of the medium near the event horizon.
We investigate the distribution of gravitational energy on the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the {\it Teleparallel Equivalent of General Relativity}, which is an alternative geometrical formulation of General Relativity, where gravity is describe by a spacetime endowed with torsion, rather than curvature, with the fundamental field variables being tetrads. We calculate the energy enclosed by a two-surface of constant radius - in particular, the energy enclosed by the event horizon of the black hole. In this case we f…
We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field, and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equa…
Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Institute of Fundamental and Applied Research, National Research University TIIAME（TIIAME国立研究型大学基础与应用研究所）；Tashkent State Technical University（塔什干国立技术大学）
We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter ${\cal B}$, and inclination angle $θ$ of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: a) regular oscillatory motion, b) destruction due to capture by the magnetized black hole, c) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time serie…
Based on the scalar-tensor-vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is stat…
Charged particle bound orbits around magnetized Schwarzschild black holes: S2 star and hotspot applications
Harbin Institute of Technology（哈尔滨工业大学）；Tashkent University of Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Universidad Central de Chile（智利中央大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Tashkent State Technical University（塔什干国立技术大学）；Urgench State University（乌尔根奇国立大学）
In the present paper, we have investigated the motion of charged particles together with magnetic dipoles to determine how well the spacetime deviation parameter $ε$ and external uniform magnetic field can mimic the spin of a rotating Kerr black hole. Investigation of charged particle motion has shown that the deviation parameter $ε$ in the absence of external magnetic fields can mimic the rotation parameter of Kerr spacetime up to $a/M \approx0.5$. The combination of external magnetic field and deviation parameter can do even a better job mimicking the rotation parameter up to $a/M\simeq0.93$…
We analyze the dispersion modes of hot plasma around Schwarzschild de-Sitter event horizon in the presence of Veselago medium. For this purpose, we apply ADM 3+1 formalism to develop GRMHD equations for the Schwarzschild de-Sitter spacetime. Implementation of linear perturbation yields perturbed GRMHD equations that are used for the Fourier analysis of rotating (non-magnetized and magnetized) plasma. Wave analysis is described by the graphical representation of the wave vector, refractive index, change in refractive index, phase and group velocities. The outcome of this work supports the valid…
We apply the ADM 3+1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It…
In this paper we have investigated the dynamics of neutral, electrically charged and magnetized particles around renormalized group improved (RGI) Schwarzschild black hole in the presence of external asymptotically uniform magnetic field. We have analyzed the spacetime structure around RGI black hole by investigating Ricci, the square of Ricci tensor and Kretschmann curvature scalars and shown that only in the case when the parameter $γ=0$ the curvature becomes infinite at the center of the black hole, while for non-zero values of $γ$ parameter the black hole curvature reflects the properties …
In many astrophysically relevant situations radiation reaction force acting upon a charge can not be neglected and the question arises about the location and stability of circular orbits in such regime. Motion of point charge with radiation reaction in flat spacetime is described by Lorenz-Dirac (LD) equation, while in curved spacetime -- by DeWitt-Brehme (DWB) equation containing the Ricci term and the tail term. We show that for the motion of elementary particles in vacuum metrics the DWB equation can be reduced to the covariant form of the LD equation which we use here. Generically, the LD …
The 3+1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number $k$. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature…
We have studied the wave properties of the cold and isothermal plasma in the vicinity of the Schwarzschild black hole event horizon. The Fourier analyzed perturbed 3+1 GRMHD equations are taken on the basis of which the complex dispersion relations are obtained for non-rotating, rotating non-magnetized and rotating magnetized backgrounds. The propagation and attenuation vectors along with the refractive index are obtained (shown in graphs) to study the dispersive properties of the medium near the event horizon. The results show that no information can be obtained from the Schwarzschild magneto…
We use the Ernst-Schwarzschild solution for a black hole immersed in a uniform magnetic field to estimate corrections to the bending angle and time delay due-to presence of weak magnetic fields in galaxies and between galaxies, and also due-to influence of strong magnetic field near supermassive black holes. The magnetic field creates a kind of confinement in space, that leads to increasing of the bending angle and time delay for a ray of light propagating in the equatorial plane.
As we know, the effect of strong magnetic field causes the anisotropy for the magnetized compact objects. Therefore, in this paper, we have studied the structure properties of anisotropic case of magnetized neutron star. We have derived the equation of state (EoS) of neutron star matter for two forms of magnetic fields, one uniform and one density dependent. We have solved the generalized Tolman Oppenheimer Volkoff equations to examine the maximum mass and corresponding radius, Schwarzschild radius, graviitational redshift, Kretschmann scalar, and Buchdahl theorem for this system. It was shown…
In order to test the role of large-scale magnetic fields in quasiperiodic oscillation phenomena observed in microquasars, we study oscillatory motion of charged particles in vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole…
In this paper, we examine the weak deflection angle and greybody bound for magnetized regular black hole.$~$ For this purpose, we apply the Gauss-Bonnet theorem on the black hole and obtain the deflection angle in plasma and non-plasma mediums.$~$ Moreover, we investigate graphically the effect of impact parameter on the deflection angle for regular black hole in both mediums. We examine that deflection angle goes to infinity when the impact parameter approaches to zero. We also observe that deflection angle shows negative behaviour at $q=0.6$ and $q=2.09$ but at $0.6<q<2.09$, angle shows the …
We present stationary solutions of geometrically thick discs (or tori) endowed with a self-consistent toroidal magnetic field distribution surrounding a non-rotating black hole in an analytical, static, spherically-symmetric $f(R)$-gravity background. These $f(R)$-gravity models introduce a Yukawa-like modification to the Newtonian potential, encoded in a single parameter $δ$ which controls the strength of the modified potential and whose specific values affect the disc configurations when compared to the general relativistic case. Our models span different magnetic field strengths, from purel…
We present a numerical study of the dynamics of magnetized, relativistic, non-self-gravitating, axisymmetric tori orbiting in the background spacetimes of Schwarzschild and Kerr black holes. The initial models have a constant specific angular momentum and are built with a non-zero toroidal magnetic field component, for which equilibrium configurations have recently been obtained. In this work we extend our previous investigations which dealt with purely hydrodynamical thick discs, and study the dynamics of magnetized tori subject to perturbations which, for the values of the magnetic field str…
We obtain a family of exact solutions describing magnetized black holes in an external gravitational field. Locally the solutions can be interpreted as representing the near-horizon region of a black hole, which interacts with a surrounding matter distribution producing a strong magnetic field. Thus, the solutions reflect the influence of both a gravitational and an electromagnetic external potential in the strong field regime. The static members in the family are generalizations of the Schwarzschild solution in the described environment, while the rotating ones generalize the magnetized Reiss…
We found quasinormal modes, both in time and frequency domains, of the Ernst black holes, that is neutral black holes immersed in an external magnetic field. The Ernst solution reduces to the Schwarzschild solution, when the magnetic field vanishes. It is found that the quasinormal spectrum for massless scalar field in the vicinity of the magnetized black holes acquires an effective "mass" $μ= 2 B m$, where m is the azimuthal number and B is parameter describing the magnetic field. We shall show that in the presence of a magnetic field quasinormal modes are longer lived and have larger oscilla…
We study the dipolar magnetic field configuration in dependence on brane tension and present solutions of Maxwell equations in the internal and external background spacetime of a magnetized spherical star in a Randall-Sundrum II type braneworld. The star is modelled as sphere consisting of perfect highly magnetized fluid with infinite conductivity and frozen-in dipolar magnetic field. With respect to solutions for magnetic fields found in the Schwarzschild spacetime brane tension introduces enhancing corrections both to the interior and the exterior magnetic field. These corrections could be r…
This work is devoted to study the effects of Einstein-Æther gravity on the dynamics of magnetized particles orbiting a static, spherically symmetric and uncharged black hole immersed in an external asymptotically uniform magnetic field in both comoving and proper observers frames. The analysis is carried out by varying the free parameters $c_{13}$ and $c_{14}$ of the Einstein-Æther theory and noticing their impacts on the particle trajectories, radii of the innermost stable circular orbits (ISCOs), and the amount of center-of-mass energy produced as a result of the collision. The strength of t…
Radiation reaction acting on a charged particle moving at a stable circular orbit of a magnetized black hole can lead to the shift of the orbital radius outwards from the black hole. The effect causes increase of the energy and angular momentum of the particle measured by an observer at rest at infinity. In this note we show that "widening" of such orbits is independent of the field configuration, however, it appears only in the cases with the external Lorentz force acting outwards from the black hole. This condition corresponds to $q L B > 0$, where $q$ and $L$ are the charge and angular mome…
By exploiting the extreme environment of the black hole (BH) as a potential place for axion-photon interaction, we use an axion-producing model of the magnetized plasma to study the shadow of an asymptotically flat rotating BH immersed into an axion-plasmon cloud. By aiming to reveal footprints of axion in the dark shadow of BH, we in this paper explore the influence of the fixed axion-plasmon background on the motion of incident photons around the rotating BH. Under some free parameter settings, we find that axion-plasmon cloud around rotating BH affects the shape and size of the shadow in su…
In this paper, geodesic motion of the charged particles in the vicinity of event horizon of Schwarzschild anti-de-Sitter black hole (BH) with topological defects has been investigated. Weakly magnetized environment is considered in the surrounding of BH which only effects the motion of the particles and doesn't effect the geometry of the BH. Hence, particles are under the influence of gravity and electromagnetic forces. We have explored the effect of magnetic field on the trajectories of the particles and more importantly on the position of the innermost stable circular orbit. It is observed t…
Testing the true nature of black holes - the no-hair hypothesis - will become increasingly more precise in the next few years as new observational data is collected in both the gravitational wave channel and the electromagnetic channel. In this paper we consider numerically generated spacetimes of Kerr black holes with synchronised scalar hair and build stationary models of magnetized thick disks (or tori) around them. Our approach assumes that the disks are not self-gravitating, they obey a polytropic equation of state, the distribution of their specific angular momentum is constant, and they…
We analytically calculate the influence of a plasma on the shadow of a black hole (or of another compact object). We restrict to spherically symmetric and static situations, where the shadow is circular. The plasma is assumed to be non-magnetized and pressure-less. We derive the general formulas for a spherically symmetric plasma density on an unspecified spherically symmetric and static spacetime. The formalism applies not only to black holes but also, e.g., to wormholes. As examples for the underlying spacetime model, we consider the Schwarzschild spacetime and the Ellis wormhole. In particu…
The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of gamma-ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equatio…
We study the linear polarization from the accretion disk around weakly and strongly naked Janis-Newman-Winicour singularities. We consider an analytical toy model of thin magnetized fluid ring orbiting in the equatorial plane and emitting synchrotron radiation. The observable polarized images are calculated and compared to the Schwarzschild black hole for physical parameters compatible with the radio source M87. For small inclination angles the direct images of the weakly naked singularities closely mimic the Schwarzschild black hole. The deviation in the polarization properties increases if w…
We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions $f(R)$, $F(R)$ and $τ_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic ($f >0$), parabolic ($f=0$) and elliptic ($f < 0$) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the …
Arnold Sommerfeld Center for Theoretical Physics（阿诺德·索末菲理论物理中心）；Univ de Lyon, ENS de Lyon, Laboratoire de Physique, CNRS UMR 5672（里昂大学，巴黎高等师范学院，物理实验室，法国国家科学研究中心）；Universidad de Tarapacá（塔拉帕卡大学）；Universidad de Concepción（康塞普西翁大学）
We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy…
