Jiří Kovář

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Pseudo-Newtonian gravitational potential introduced in spherically symmetric black-hole spacetimes with a repulsive cosmological constant is tested for equilibrium toroidal configurations of barotropic perfect fluid orbiting the black holes. Shapes and potential depths are determined for the marginally stable barotropic tori with uniform distribution of specific angular momentum, using both the pseudo-Newtonian and fully relativistic approach. For the adiabatic (isoentropic) perfect fluid, temperature profiles, mass-density and pressure profiles and total masses of pseudo-Newtonian and relativistic tori are compared providing important information on the relevance of the test-disc approximation in both the approaches. It is shown that the pseudo-Newtonian approach can be precise enough and useful for the modelling of accretion discs in the Schwarzschild-de Sitter spacetimes with the cosmological parameter y=Lambda M^(2)/3 < 10^(-6). For astrophysically relevant black holes with y<10^(-25), this statement is tested and shown to be precise in few percent for both accretion and excretion tori and for the marginally bound, i.e., maximally extended tori allowing simultaneous inflow to the black hole and outflow to the outer space.

TRANSITION FROM REGULAR TO CHAOTIC CIRCULATION IN MAGNETIZED CORONAE NEAR COMPACT OBJECTS

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 (RPs) and we compare them with Poincare surfaces of section. We describe the RPs in terms of the recurrence quantification analysis, 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 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.

Off-equatorial orbits in strong gravitational fields near compact objects?II: halo motion around magnetic compact stars and magnetized black holes

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.

Kinetic Theory of Equilibrium Axisymmetric Collisionless Plasmas in Off-equatorial Tori around Compact Objects

The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.

CHARGED TORI IN SPHERICAL GRAVITATIONAL AND DIPOLAR MAGNETIC FIELDS

A Newtonian model of non-conductive, charged, perfect fluid tori orbiting in combined spherical gravitational and dipolar magnetic fields is presented and stationary, axisymmetric toroidal structures are analyzed. Matter in such tori exhibits a purely circulatory motion and the resulting convection carries charges into permanent rotation around the symmetry axis. As a main result, we demonstrate the possible existence of off-equatorial charged tori and equatorial tori with cusps that also enable outflows of matter from the torus in the Newtonian regime. These phenomena qualitatively represent a new consequence of the interplay between gravity and electromagnetism. From an astrophysical point of view, our investigation can provide insight into processes that determine the vertical structure of dusty tori surrounding accretion disks.

Equilibrium conditions of spinning test particles in Kerr–de Sitter spacetimes

Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr–de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant cases of equilibrium positions in the equatorial plane and on the symmetry axis of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes. In the equatorial plane, it is possible at the so-called static radius, where the gravitational attraction is balanced by the cosmic repulsion, for the spinless particles as well as for spinning particles with arbitrarily large -oriented spin or at any radius outside the ergosphere with a specifically given spin orthogonal to the equatorial plane. On the symmetry axis, the equilibrium is possible at any radius in the stationary region and is given by an appropriately tuned spin directed along the axis. At the static radii on the axis the spin of particles in equilibrium must vanish.

Regular and chaotic orbits near a massive magnetic dipole

Within the framework of Bonnors 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 Poincare 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 Stormers 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.

Electrically charged matter in rigid rotation around magnetized black hole

We study charged-fluid toroidal structures surrounding a non-rotating charged black hole immersed in a large-scale, asymptotically uniform magnetic field. In continuation of our former study on electrically charged matter in approximation of zero conductivity, we demonstrate existence of orbiting structures in permanent rigid rotation in the equatorial plane, and charged clouds hovering near the symmetry axis. We constrain the range of parameters that allow stable configurations and derive the geometrical shape of equi-pressure surfaces. Our simplified analytical study suggests that these regions of stability may be relevant for trapping electrically charged particles and dust grains in some areas of the black hole magnetosphere, being thus important in some astrophysical situations.

Recurrence plots and chaotic motion around Kerr black hole

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 Poincare 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. c...

FORCES IN KERR SPACE–TIMES WITH A REPULSIVE COSMOLOGICAL CONSTANT

Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black hole and naked-singularity space–times with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being nonzero. The space–times are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish.