Zdeněk Stuchlík

Equatorial circular orbits in the Kerr–de Sitter spacetimes

Equatorial motion of test particles in Kerr\char21{}de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both black-hole and naked-singularity spacetimes, and their relevance for thin accretion disks is established. The circular orbits constitute two families that coalesce at the so-called static radius. The orientation of the motion along the circular orbits is, in accordance with case of asymptotically flat Kerr spacetimes, defined by relating the motion to the locally nonrotating frames. The minus-family orbits are all counterrotating, while the plus-family orbits are usually corotating relative to these frames. However, the plus-family orbits become counterrotating in the vicinity of the static radius in all Kerr\char21{}de Sitter spacetimes, and they become counterrotating in the vicinity of the ring singularity in Kerr\char21{}de Sitter naked-singularity spacetimes with a low enough rotational parameter. In such spacetimes, the efficiency of the conversion of the rest energy into heat energy in the geometrically thin plus-family accretion disks can reach extremely high values exceeding the efficiency of the annihilation process. The transformation of a Kerr\char21{}de Sitter naked singularity into an extreme black hole due to accretion in the thin disks is briefly discussed for both the plus-family and minus-family disks. It is shown that such a conversion leads to an abrupt instability of the innermost parts of the plus-family accretion disks that can have strong observational consequences.

Profiles of emission lines generated by rings orbiting braneworld Kerr black holes

In the framework of the braneworld models, rotating black holes can be described by the Kerr metric with a tidal charge representing the influence of the non-local gravitational (tidal) effects of the bulk space Weyl tensor onto the black hole spacetime. We study the influence of the tidal charge onto profiled spectral lines generated by radiating tori orbiting in vicinity of a rotating black hole. We show that with lowering the negative tidal charge of the black hole, the profiled line becomes to be flatter and wider keeping their standard character with flux stronger at the blue edge of the profiled line. The extension of the line grows with radius falling and inclination angle growing. With growing inclination angle a small hump appears in the profiled lines due to the strong lensing effect of photons coming from regions behind the black hole. For positive tidal charge (b > 0) and high inclination angles two small humps appear in the profiled lines close to the red and blue edge of the lines due to the strong lensing effect. We can conclude that for all values of b, the strongest effect on the profiled lines shape (extension) is caused by the changes of the inclination angle.

Appearance of Keplerian discs orbiting Kerr superspinars

We study optical phenomena related to the appearance of Keplerian accretion discs orbiting Kerr superspinars predicted by string theory. The superspinar exterior is described by standard Kerr naked singularity geometry breaking the black hole limit on the internal angular momentum (spin). We construct local photon escape cones for a variety of orbiting sources that enable us to determine the superspinars silhouette in the case of distant observers. We show that the superspinar silhouette depends strongly on the assumed edge where the external Kerr spacetime is joined to the internal spacetime governed by string theory and significantly differs from the black hole silhouette. The appearance of the accretion disc is strongly dependent on the value of the superspinar spin in both their shape and frequency shift profile. Apparent extension of the disc grows significantly with the growing spin, while the frequency shift grows with the descending spin. This behaviour differs substantially from the appearance of discs orbiting black holes enabling thus, at least in principle, to distinguish clearly the Kerr superspinars and black holes. In vicinity of a Kerr superspinar the non-escaped photons have to be separated to those captured by the superspinar and those being trapped in its strong gravitational field leading to self-illumination of the disc that could even influence its structure and cause self-reflection effect of radiation of the disc. The amount of trapped photons grows with descending superspinar spin. We thus can expect significant self-illumination effects in the field of Kerr superspinars with near-extreme spin a ~ 1.

Ultra-high-energy collisions in the superspinning Kerr geometry

Kerr naked singularities (superspinars) have to be efficiently converted to a black hole due to accretion from Keplerian discs. In the final stages of the conversion process the near-extreme Kerr naked singularities (superspinars) provide a variety of extraordinary physical phenomena. Such superspinning Kerr geometries can serve as an efficient accelerator for extremely high-energy collisions enabling direct and clear demonstration of the outcomes of the collision processes. We shall discuss the efficiency and visibility of the ultra-high-energy collisions in the deepest parts of the gravitational well of superspinning near-extreme Kerr geometries for the whole variety of particles freely falling from infinity. We demonstrate that the ultra-high-energy processes can be obtained with no fine tuning of the motion constants and the products of the collision can escape to infinity with both directional and energetical efficiency significantly higher than in the case of the near-extreme black holes. The strongest efficiency of the collision process is reached for particles falling along trajectories with maximally acceptable negative angular momentum.

Relativistic thick discs in the Kerr–de Sitter backgrounds

Perfect fluid tori with a uniform distribution of the specific angular momentum, ?(r, ?) = const, orbiting the Kerr?de Sitter black holes or naked singularities are studied. It is well known that the structure of equipotential surfaces of such marginally stable tori reflects the basic properties of any tori with a general distribution of the specific angular momentum. Closed equipotential surfaces corresponding to stationary thick discs are allowed only in the spacetimes admitting stable circular geodesics. The last closed surface crosses itself in the cusp(s) enabling the outflow of matter from the torus due to the violation of hydrostatic equilibrium. The inner cusp enables an accretion onto the central object. The influence of the repulsive cosmological constant, ? > 0, on the equipotential surfaces lies in the existence of the outer cusp (with a stabilizing effect on the thick discs) and in the strong collimation of open equipotential surfaces along the rotational axis. Both the effects take place near a so-called static radius where the gravitational attraction is just balanced by the cosmic repulsion. The outer cusp enables excretion, i.e., the outflow of matter from the torus into the outer space. The plus-family discs (which are always co-rotating in the black-hole backgrounds but can be counter-rotating, even with negative energy of the fluid elements, in some naked-singularity backgrounds) are thicker and more extended than the minus-family ones (which are always counter-rotating in all backgrounds). For co-rotating discs in the naked-singularity spacetimes, the potential well between the centre of the disc and its edges at the cusps is usually much higher than in the black-hole spacetimes. If the parameters of naked-singularity spacetimes are very close to the parameters of extreme black-hole spacetimes, the family of possible disc-like configurations includes members with two isolated discs where the inner one is always a counter-rotating accretion disc.

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.

INFLUENCE OF THE RELICT COSMOLOGICAL CONSTANT ON ACCRETION DISCS

Surprisingly, the relict cosmological constant has a crucial influence on properties of accretion discs orbiting black holes in quasars and active galactic nuclei. We show it by considering basic properties of both the geometrically thin and thick accretion discs in the Kerr–de Sitter black hole (naked-singularity) spacetimes. Both thin and thick discs must have an outer edge allowing outflow of matter into the outer space, located nearby the so-called static radius, where the gravitational attraction of a black hole is balanced by the cosmological repulsion. Jets produced by thick discs can be significantly collimated after crossing the static radius. Extension of discs in quasars is comparable with extension of the associated galaxies, indicating a possibility that the relict cosmological constant puts an upper limit on extension of galaxies.

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.

Observational phenomena related to primordial Kerr superspinars

String theory indicates the existence of primordial Kerr superspinars, extremely compact objects with exterior described by the Kerr naked-singularity geometry. The primordial superspinars have to be converted to a black hole due to accretion, but they could survive to the era of high-redshift quasars. We discuss observational phenomena caused by the primordial Kerr superspinars in this era, considering the properties of corotating Keplerian accretion discs orbiting such superspinars and the optical phenomena modified by their presence. The potential well around a near-extreme superspinar with spin a very close to the extreme black hole value a = 1 is very deep so that the efficiency of the accretion process reaches 157.7%, influencing thus significantly the spectral continuum of corotating Keplerian discs and giving a signature of near-extreme superspinars. Such superspinars can also serve as an efficient accelerator for extremely high-energy collisions. Phenomena enabling a clear distinction of primordial Kerr superspinars and black holes are related to the disc oscillations with the radial and vertical epicyclic frequencies and the most profound could be differences implied by the profiled spectral lines generated in the innermost parts of the corotating Keplerian discs.

Influence of the cosmological constant on the motion of Magellanic Clouds in the gravitational field of Milky Way

Using the pseudo-Newtonian (PN) potential reflecting properties of the Schwarz-schild-de Sitter spacetime, we estimate the influence of the repulsive cosmological constant ? ~ 1.3 ? 10?56cm?2 implied by recent cosmological tests onto the motion of both Small and Large Magellanic Clouds (SMC and LMC) in the gravitational field of the Milky Way. Considering detailed modelling of the gravitational field of the Galaxy disc, bulge and cold dark matter halo, the trajectories of SMC and LMC constructed for the PN potential with the cosmological constant are confronted to those given for ? = 0. In the realistic model of the extended cold dark matter halo its edge and related total mass are taken at typical values reflecting recent diversity in the total Galaxy mass estimates. In all cases, strong influence of the cosmological constant, on 10% level or higher, has been found for motion of both SMC and LMC. Inside the halo, the Newtonian part of the PN potential is exact enough, while outside the halo the PN potential can give relevant relativistic corrections. The role of the cosmological constant is most conspicuous when binding mass is estimated for the satellite galaxies. We have found a strong influence of cosmic repulsion on the total binding mass for both galaxies. For SMC there is the binding mass MSMC? = 0 = 7.07 ? 1011M? and MSMC? > 0 = 8.61 ? 1011M?, while even much higher increase is found for LMC, where MLMC? = 0 = 1.50 ? 1012M? and MLMC? > 0 = 2.21 ? 1012M?, putting serious doubts on the possibility that the LMC is bounded by the Milky Way. However, the estimates of binding masses are strongly influenced by initial velocity of SMC and LMC; we took the values inferred for the IAU MW rotation velocity ~ 220 km/s. Our results indicate very important role of the cosmic repulsion in the motion of interacting galaxies, clearly demonstrated in the case of the satellite SMC and LMC galaxies moving in the field of Milky Way. In some cases, the effect of the cosmic repulsion can be even comparable to the effects of the dynamical friction and the Andromeda Galaxy.