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According to General Relativity, astrophysical black holes are described by a small number of parameters. Apart from the mass of the black hole (M), among the most interesting characteristics is the spin (a), which determines the degree of rotation, i.e., the angular momentum of the black hole. The latter is observationally constrained by the spectral and timing properties of the radiation signal emerging from an accretion disk of matter orbiting near the event horizon. In the case of planar (standard, equatorial) accretion disk, it is the location of the Innermost Stable Circular Orbit (ISCO) that determines the observable radiation characteristics, and this way allows us to measure the spin. In this paper, we discuss a more general case of the Innermost Stable Spherical Orbits (ISSO) extending above and below the equatorial plane. To this end, we study the non-equatorial geodesic motion of particles following inclined, spherical, relativistically precessing trajectories with the aim of exploring the boundary between the regions of stable (energetically bound) and escaping (energetically unbound) motion. The concept of the ISSO radius should play a role in determining the inner rim of a tilted or geometrically thick accretion flow. We demonstrate that the region of inclined bound orbits has a complicated structure due to enhanced precession near the inner rim. We also explore the fate of particles launched below the radius of the Marginally Bound Spherical Orbit (MBSO): these may either plunge into the event horizon or escape to radial infinity., Comment: Accepted for publication in ApJ; 23 pages, 22 figures. Revised version with corrected colours in Figure 2

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs., Comment: 17 pages, 9 figures

Combined influence of rotation of a black hole and ambient magnetic fields creates conditions for powerful astrophysical processes of accretion and outflow of matter which are observed in many systems across the range of masses; from stellar-mass black holes in binary systems to supermassive black holes in active galactic nuclei. We study a simplified model of outflow of electrically charged particles from the inner region of an accretion disk around a spinning (Kerr) black hole immersed in a large-scale magnetic field. In particular, we consider a non-axisymmetric magnetosphere where the field is misaligned with the rotation axis. In this contribution we extend our previous analysis of acceleration of jet-like trajectories of particles escaping from bound circular orbits around a black hole. While we have previously assumed the initial setup of prograde (co-rotating) orbits, here we relax this assumption and we also consider retrograde (counter-rotating) motion. We show that the effect of counter-rotation may considerably increase the probability of escape from the system, and it allows more efficient acceleration of escaping particles to slightly higher energies compared to the co-rotating disk., Comment: 11 pages, 6 figures; to appear in proceedings of 16th Marcel Grossmann Meeting, Session PT5 "Dragging is never draggy: MAss and CHarge flows in GR'' (id. #393), 5-10 July 2021

We study the effects of large scale magnetic fields on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on geodesic orbits in the equatorial plane become ionized, and hence they are destabilized by the charging process. Fraction of charged particles are then accelerated out of the equatorial plane and then follow jet like trajectories with relativistic velocities. We explore non axisymmetric systems in which the magnetic field is inclined with respect to the black hole spin. We study the system numerically in order to locate the zones of escaping trajectories and compute the terminal escape velocity. By breaking the axial symmetry we notice increasing fraction of unbound orbits which allow for acceleration to ultrarelativistic velocities., Comment: 7 pages, 3 figures; to appear in Proceedings of IWARA2020 - 9th International Workshop on Astronomy and Relativistic Astrophysics (on-line, 6-12 of September 2020), https://indico.cern.ch/event/822124/contributions/3970054/

Strong gravity and magnetic fields are key ingredients that power processes of accretion and ejection near compact objects. While the particular mechanisms that operate here are still discussed, it seems that the presence of an ordered magnetic field is crucial for the acceleration and collimation of relativistic jets of electrically charged particles on superhorizon length scales. In this context, we further study the effect of a large-scale magnetic field on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on regular geodesic orbits in the equatorial plane are destabilized by a charging process (e.g., by photoionization). Some charged particles are accelerated out of the equatorial plane, and they follow jetlike trajectories with relativistic velocities. In our previous paper, we investigated this scenario for the case of perfect alignment of the magnetic field with the axis of rotation; i.e., the system was considered axisymmetric. Here we relax this assumption and investigate nonaxisymmetric systems in which the magnetic field is arbitrarily inclined with respect to the black hole spin. We study the system numerically in order to locate the zones of escaping trajectories and compute the maximum (terminal) escape velocity. It appears that breaking the axial symmetry (even by small inclination angles) substantially increases the fraction of escaping orbits and allows the acceleration to ultrarelativistic velocities that were excluded in the axisymmetric setup. The presence of transient chaotic dynamics in the launching region of the relativistic outflow is confirmed with chaotic indicators., Comment: 14 pages, 8 figures; accepted for publication in ApJ; revised version with typographical and language corrections

Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source., Comment: 18 pages, 14 figures

Relativistic effects of compact objects onto electromagnetic fields in their vicinity are investigated using the test-field approximation. In particular, we study the possible emergence of magnetic null points which are astrophysically relevant for the processes of magnetic reconnection. While the magnetic reconnection occurs in the presence of plasma and may lead to violent mass ejection, we show here that strong gravitation of the supermassive black hole may actively support the process by suitably entangling the field lines even in the electro-vacuum description. In this contribution we further discuss the case of a dipole-type magnetic field of the neutron star on the plunging trajectory to the supermassive black hole. While we have previously shown that given model in principle admits the formation of magnetic null points, here we explore whether and where the null points appear for the astrophysically relevant values of the parameters., Comment: 10 pages, 5 figures; to appear in the RAGtime conference proceedings (Opava, October 15-19 2018)

We discuss the effects of electric charging on the equilibrium configurations of magnetized, rotating fluid tori around black holes of different mass. In the context of gaseous/dusty tori in galactic nuclei, the central black hole dominates the gravitational field and it remains electrically neutral, while the surrounding material acquires some electric charge and exhibits non-negligible self-gravitational effect on the torus structure. The structure of the torus is influenced by the balance between the gravitational and electromagnetic forces. A cusp may develop even in Newtonian tori due to the charge distribution., Comment: 5 pages, 1 figure; to appear in Proceedings of the 15th Marcel Grossman Meeting on General Relativity - the session AC3 on "Accretion Discs and Jets" by Eva Hackmann & Audrey Trova (Rome, 1-7 July 2018), edited by Elia Battistelli, Robert T. Jantzen, and Remo Ruffini, in preparation

Magnetic null points can develop near the ergosphere boundary of a rotating black hole by the combined effects of strong gravitational field and the frame-dragging mechanism. The electric component does not vanish in the magnetic null and an efficient process or particle acceleration can occur. The situation is relevant for starving (low-accretion-rate, such as the Milky Way's supermassive black hole) nuclei of some galaxies which exhibit only episodic accretion events. The presence of the magnetic field field of an external origin is an important aspect. We propose that such conditions can develop when a magnetized neutron star approaches the supermassive black hole during late stages of its inspiral motion. The field lines of the neutron star dipole thread the black hole's event horizon and change rapidly their connectivity. We put in comparison the case of a dipole-type magnetic field of a sinking and orbiting star near a non-rotating black hole, and the near-horizon structure of an asymptotically uniform magnetic field of a distant source near a fast-rotating black hole. Although the two cases are qualitatively different from each other, they both develop magnetically neutral null points near the event horizon., Comment: 5 pages, 3 figures; to appear in Proceedings of IWARA2018 - 8th International Workshop on Astronomy and Relativistic Astrophysics (Ollantaytambo, 8-15 September 2018), in preparation

We explore the structure of a dipole-type vacuum field of a slowly rotating magnetic star near the horizon of a supermassive black hole, where the structure of field lines becomes highly distorted by effects of strong gravity. Such a situation may occur near a neutron star in the final stages of a plunging trajectory into a galactic center. We solve Maxwell's equations in the Rindler approximation for the rotating conducting source of dipolar magnetic field arbitrarily inclined with respect to the axis of rotation. For the fixed inclination angle we calculate the field including the radiative terms while in the general case we discuss the electromagnetic field considering the near-field terms only. In the latter case we investigate the emergence of magnetic null points within the vacuum magnetosphere. Null points become highly relevant in the presence of astrophysical plasma where they are connected with processes of magnetic reconnection and mass ejection., Comment: 12 pages, 10 figures; published in Physical Review D; final version with language corrections and updated bibliography

An interplay of magnetic fields and gravitation drives accretion and outflows near black holes. However, a specific mechanism is still a matter of debate; it is very likely that different processes dominate under various conditions. In particular, for the acceleration of particles and their collimation in jets, an ordered component of the magnetic field seems to be essential. Here we discuss the role of large-scale magnetic fields in transporting the charged particles and dust grains from the bound orbits in the equatorial plane of a rotating (Kerr) black hole and the resulting acceleration along trajectories escaping the system in a direction parallel to the symmetry axis (perpendicular to the accretion disk). We consider a specific scenario of destabilization of circular geodesics of initially neutral matter by charging (e.g., due to photoionization). Some particles may be set on escaping trajectories and attain relativistic velocity. The case of charged particles differs from charged dust grains by their charge-to-mass ratio, but the acceleration mechanism operates in a similar manner. It appears that the chaotic dynamics controls the outflow and supports the formation of near-horizon escape zones. We employ the technique of recurrence plots to characterize the onset of chaos in the outflowing medium. We investigate the system numerically and construct the basin-boundary plots, which show the location and the extent of the escape zones. The effects of black hole spin and magnetic field strength on the formation and location of escape zones are discussed, and the maximal escape velocity is computed., Comment: 12 pages, 10 figures; published in ApJ; revised version with typographical and language corrections

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr spacetime, when deterministic chaos and different levels of stochastic noise are present. In particular, we suggest a recurrence-based criterion to reveal whether the time series comes from a deterministic source and find a noise-level threshold of its applicability., Comment: 16 pages, 6 figures

Black holes cannot support their own internal magnetic field like, for example, compact stars can. Despite this fact observations indicate that event horizons of supermassive black holes (SMBH) are threaded by field lines along which plasma streams flow. Various magnetohydrodynamical mechanisms have been suggested to generate turbulent magnetic fields on small scales, however, the origin of the large-scale component is unclear. In this write-up we describe our progress in an on-going work and discuss the possibility of dipole-type magnetic fields being brought onto SMBH by magnetized neutron stars, which are expected to drift inward from a hidden population in the Nuclear Star Cluster. This can contribute to an organised component of the magnetic field on the characteristic length-scale of the stellar size, which thread the horizon during the final stages of the magnetized star plunge into or its close flyby around SMBH. Because of mass--size scaling relations for black holes, the effect is more important for lower-mass SMBH., Comment: 9 pages, 2 figures; to appear in Proceedings of the 14th INTEGRAL/BART Workshop in Karlovy Vary (Czech Republic, 3-7 April 2017)

Dynamics of charged matter in the oblique black hole magnetosphere is investigated. In particular, we adopt a model consisting of a rotating black hole embedded in the external large-scale magnetic field that is inclined arbitrarily with respect to the rotation axis. Breaking the axial symmetry appears to have profound consequences regarding the dynamics of particles and it also poses some methodological difficulties. In this contribution we discuss the applicability of the method of effective potential for the non-axisymmetric model and show that it may only be applied in the appropriate reference frame., Comment: 6 pages, 2 figures; to appear in the Proceedings of the "14th Marcel Grossmann Meeting" (Rome, July 12 - 18, 2015)

We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the performance of the symplectic integrator with several non-symplectic routines and discuss under which circumstances we should choose the symplectic one and when we should switch to some other scheme. We are basically concerned with two crucial, yet opposing aspects - accuracy of the integration and CPU time consumption. The latter is generally less critical in our application while the highest possible accuracy is strongly demanded., Comment: 11 pages, 5 figures, 2 tables, prepared in 2011 for the Proceedings of RAGtime 10-13: Workshops on black holes and neutron stars (Opava, September 15 - 17, 2010)

Dynamics of charged particles in the vicinity of a rotating black hole embedded in the external large-scale magnetic field is numerically investigated. In particular, we consider a non-axisymmetric model in which the asymptotically uniform magnetic field is inclined with respect to the axis of rotation. We study the effect of inclination onto the prevailing dynamic regime of particle motion, i.e. we ask whether the inclined field allows regular trajectories or if instead, the deterministic chaos dominates the motion. In this contribution we further discuss the role of initial condition, particularly, the initial azimuthal angle. To characterize the measure of chaoticness we compute maximal Lyapunov exponents and employ the method of Recurrence Quantification Analysis., Comment: 6 pages, 4 figures; to appear in the Proceedings of The Spanish Relativity Meeting ERE 2014 (Valencia, September 1 - 5, 2014)

Magnetic null points can develop near the ergosphere boundary of a rotating black hole by the combined effects of strong gravitational field and the frame-dragging mechanism. The induced electric component does not vanish an efficient process of particle acceleration can occur. Furthermore, the effect of imposed (weak) magnetic field can trigger an onset of chaos. The model set-up appears to be relevant for low-accretion-rate nuclei of some galaxies which exhibit episodic accretion events (such as the Milky Way's supermassive black hole) embedded in a large-scale magnetic field of external origin. We review our recent results and we give additional context for future work with the focus on the role of gravito-magnetic effects caused by rotation of the black hole. While the test motion is strictly regular in the classical black hole space-time, with and without effects of rotation or electric charge, gravitational perturbations and imposed external electromagnetic fields may lead to chaos., Comment: write-up of a talk at 11th INTEGRAL/BART Workshop in Karlovy Vary (Czech Republic, 22-25 April 2014); 13 pages, 11 figures (resolution downgraded to reduce the file size; for full resolution see the journal paper)

Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable motion. We also investigate situations when the particle dynamics exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincar\'e surfaces of section and of recurrence plots., Comment: 11 pages, 6 figures, published in the proceedings of the conference "Relativity and Gravitation: 100 Years after Einstein in Prague" (25. - 29. 6. 2012, Prague)

While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr--Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consider the presence of a weak, ordered, large-scale magnetic field. An axially-symmetric model consisting of a rotating black hole embedded in an aligned magnetic field is generalized by allowing an oblique direction of the field having a general inclination, with respect to the rotation axis of the system. The inclination of the field acts as an additional perturbation to the motion of charged particles as it breaks the axial symmetry of the system and cancels the related integral of motion. The axial component of angular momentum is no longer conserved and the resulting system thus has three degrees of freedom. Our primary concern within this contribution is to find out how sensitive the system of bound particles is to the inclination of the field. We employ the method of the maximal Lyapunov exponent to distinguish between regular and chaotic orbits and to quantify their chaoticity. We find that even a small misalignment induces chaotic motion., Comment: 13 pages, 5 figures; published in ApJ; revised version with language and formatting corrections

Magnetic field can be amplified and twisted near a supermassive black hole residing in a galactic nucleus. At the same time magnetic null points develop near the horizon. We examine a large-scale oblique magnetic field near a rotating (Kerr) black hole as an origin of magnetic layers, where the field direction changes abruptly in the ergosphere region. In consequence of this, magnetic null points can develop by purely geometrical effects of the strong gravitational field and the frame-dragging mechanism. We identify magnetic nulls as possible sites of magnetic reconnection and suggest that particles may be accelerated efficiently by the electric component. The situation we discuss is relevant for starving nuclei of some galaxies which exhibit episodic accretion events, namely, Sagittarius A* black hole in our Galaxy., Comment: 13 pages, 5 figures, International Journal of Astronomy and Astrophysics, accepted

Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling the existence of stable circular orbits confined to the equatorial plane and of those levitating above the equatorial plane. Constructing Poincar\'e surfaces of section and recurrence plots, we also investigate the dynamics of particles moving along general off-equatorial trajectories bound in effective potential wells forming around the stable circular orbits. We demonstrate that the motion in the Bonnor spacetime is not integrable. This extends previous investigations of generalized St\"ormer's problem into the realm of exact solutions of Einstein-Maxwell equations, where the gravitational and electromagnetic effects play a comparable role on the particle motion., Comment: 27 pages, 14 figures

We discuss the role of general relativity frame dragging acting on magnetic field lines near a rotating (Kerr) black hole. Near ergosphere the magnetic structure becomes strongly influenced and magnetic null points can develop. We consider aligned magnetic fields as well as fields inclined with respect to the rotation axis, and the two cases are shown to behave in profoundly different ways. Further, we construct surfaces of equal values of local electric and magnetic intensities, which have not yet been discussed in the full generality of a boosted rotating black hole., Comment: to appear in the proceedings of "The Central Kiloparsec in Galactic Nuclei (AHAR 2011)", Journal of Physics: Conference Series (JPCS), IOP Publishing

Understanding the mechanisms of particle acceleration from the vicinity of black holes poses a challenge. Electromagnetic effects are thought to be a prime suspect, but details still need an explanation. To this end, we study a three-dimensional structure of oblique magnetic fields near a rotating black hole in vacuum. It has been proposed that such a set-up can lead to efficient acceleration when plasma is injected near a magnetic null point. We focus our attention especially on the magnetic field in the immediate neighborhood of the magnetic null point, which was previously shown to occur in the equatorial plane. By employing the Line-Integral-Convolution (LIC) method, we visualize the magnetic field lines and explore the electric lines rising out of the equatorial plane. We show the magnetic field structure near the boundary of ergosphere, depending on the spin of the black hole. Electric field develops a non-vanishing component passing through the magnetic null point and ensuring efficient acceleration of charged particles from this particular location near horizon. We also examine the effect of translatory boost on the field lines. Similarly to the frame-dragging by rotation, the linear motion carries field lines along with the black hole. Position of the magnetic null point recedes from the black hole horizon as the spin parameter increases. For the extreme value of a=1 the null point can occur outside the ergosphere., Comment: 13 pages, 8 figures, Classical and Quantum Gravity accepted

Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in relativity. For the first time, we apply recurrence plots as a suitable technique to quantify the degree of chaoticness near a black hole., Comment: PhD Thesis, 123 pages

We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase space, which is a major advantage of this approach when compared to the "traditional" methods of the numerical analysis of dynamical systems (for instance the visual survey of Poincar\'{e} surfaces of section, evaluation of the Lyapunov spectra etc.). We show that RPs and their quantitative measures (obtained from recurrence quantification analysis -- RQA) are powerful tools to detect dynamical regime of motion (regular vs. chaotic) and precisely locate the transitions between these regimes., Comment: 10 pages, 10 figures, published

Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the Recurrence Plots (RP) and we compare them with Poincar\'e surfaces of section. We describe the Recurrence Plots in terms of the Recurrence Quantification Analysis (RQA), which allows us to identify the transition between different dynamical regimes. We demonstrate that this new technique is able to detect the chaos onset very efficiently, and to provide its quantitative measure. The chaos typically occurs when the conserved energy is raised to a sufficiently high level that allows the particles to traverse the equatorial plane. We find that the role of the black-hole spin in setting the chaos is more complicated than initially thought., Comment: 21 pages, 20 figures, accepted to ApJ

Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the two-dimensional effective potential which correspond to the stable halo orbits. Here, we relax previous assumptions of the pseudo-Newtonian approach for the gravitational field of the central body and study properties of the halo orbits in detail. Within the general relativistic approach, we carry out our calculations in two cases. Firstly, we examine the case of a rotating magnetic compact star. Assuming that the magnetic field axis and the rotation axis are aligned with each other, we study the orientation of motion along the stable halo orbits. In the poloidal plane, we also discuss shapes of the related effective potential halo lobes where the general off-equatorial motion can be bound. Then we focus on the halo orbits near a Kerr black hole immersed in an asymptotically uniform magnetic field of external origin. We demonstrate that, in both the cases considered, the lobes exhibit two different regimes, namely, one where completely disjoint lobes occur symmetrically above and below the equatorial plane, and another where the lobes are joined across the plane. A possible application of the model concerns the structure of putative circumpulsar discs consisting of dust particles. We suggest that the particles can acquire a small (but non-zero) net electric charge, and this drives them to form the halo lobes., Comment: 24 pages, 7 figures

Magnetic layers are narrow regions where the field direction changes sharply. They often occur in the association with neutral points of the magnetic field. We show that an organised field can produce these structures near a rotating black hole, and we identify them as potential sites of magnetic reconnection. To that end we study the field lines affected by the frame-dragging effect, twisting the magnetic structure and changing the position of neutral points. We consider oblique fields in vacuum. We also include the possibility of translational motion of the black hole which may be relevant when the black hole is ejected from the system. The model settings apply to the innermost regions around black holes with the ergosphere dominated by a super-equipartition magnetic field and loaded with a negligible gas content., Comment: 10 pages, 3 figures, Classical and Quantum Gravity accepted