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**ABSTRACTS**

**Author: **Iryna Bormotova (Joint Institute for Nuclear Research, Dubna, Russia; Silesian University in Opava, Czech Republic)

**Title: ***Geodesic motion of test particles in Korkina-Grigoryev metric *

We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under which the finite motion of particles occurs. From the behavior of the potential curves the radii of both stable and unstable circular orbits around a black hole are found, as well as the corresponding energies of the test particles. The effective-potential curves for the Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are compared. It is shown, that in the case of the Korkina-Grigoryev metric the stable orbits eventually vanish with increasing charge.

**Author: ** Zdeněk Stuchlík (Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Czech Republic)

**Co-authors: **Z. Stuchlík, J. Schee, B. Toshmatov, J.Hladík, and J. Novotný

**Title: ***Trapping polytropic spheres as models of Galactic halos containing central supermassive black holes*

We demonstrate that polytropic spheres in spacetimes with relict cosmological constant can represent models of dark matter galactic halos. If such polytropes contain a region of trapped null geodesics extended around radius of the stable null circular geodesic, the central trapping region of these polytropes becomes gravitationally unstable and can be converted into a central supermassive black hole. The trapping polytropes can thus represent a model explaining supermassive central black holes in galactic halos, created in relatively early phases of the expansion of the Universe.

**Author: **Pavlína Jalůvková (Joint Institute for Nuclear Research, Dubna, Russia; Silesian University in Opava, Czech Republic)

**Title: ***The generalized LTB solutions in modeling the cosmological black holes*

In spite of the numerous attempts to close the discussion about the influence of cosmological expansion on local gravitationally bounded systems, this question arises in literature again and again and remains still far from its final resolution. Here one of the main problems is the problem of obtaining a physically adequate model of strongly gravitating object immersed in non-static cosmological background. Such objects are usually called ‘cosmological’ black holes and are of great interest in wide set of cosmological and astrophysical areas.

In this work the set of new exact solutions of the Einstein equations is derived for the flat space that generalizes the known Lemaitre-Tolman-Bondi solution for the case of nonzero pressure. The solutions obtained are pretending to describe the black hole immersed in nonstatic cosmological background and give a possibility to investigate the hot problems concerning the effects of the cosmological expansion in gravitationally bounded systems, the structure formation in the early universe, black hole thermodynamics and other related problems.

It is shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space.

It is demonstrated that the approach of the mass function use in solving of the Einstein equations allows clear physical interpretation of the resulting solutions, that is of much benefit to any their concrete application.

**Author: **Elena M. Kopteva (Joint Institute for Nuclear Research, Dubna, Russia)

**Co-authors: **E. M. Kopteva, P. Jalůvková, Z. Stuchlík

**Title: ***Particle and Photon Trajectories near the Black Hole Immersed in the Nonstatic Cosmological Background*

The question of constructing a consistent model of the cosmological black hole remains to be unsolved and still attracts the interest of cosmologists as far as it is important in a wide set of research problems including the problem of the black hole horizon dynamics, the problem of interplay between cosmological expansion and local gravity, the problem of structure formation in the early universe etc. In this work, the model of the cosmological black hole is built on the basis of the exact solution of the Einstein equations for the spherically symmetric inhomogeneous dust distribution in the approach of the mass function use. Possible trajectories for massive particles and photons near the black hole immersed in the nonstatic dust cosmological background are investigated in frame of the obtained model. The reference system of distant galaxy comoving to cosmological expansion combined with curvature coordinates is used, so that the resulting metric becomes nondiagonal and involves both proper ‘cosmological’ time and curvature spatial coordinates. For this metric the geodesic equations are analyzed for the test particles and photons, and the respective trajectories are built.

**Author: **Martin Kološ (Silesian University in Opava, Czech Republic)

**Title: ***Charged particle motion around magnetized black hole *

We study dynamics of charged test particles in vicinity of a black hole immersed into an asymptotically uniform external magnetic field. Real magnetic field around black hole will be far away from to be completely regular and uniform, uniform magnetic field is used as linear approximation only. Charged particle oscillations, stability of circular orbits, ionized particle acceleration and accretion disk destruction will be presented.

**Author: **Arman Tursunov (Silesian University in Opava, Czech Republic)

**Title: ***Synchrotron radiation-reaction in curved spacetime *

Combined effect of strong gravity and electromagnetic fields on the dynamics of radiating charged particles can significantly change the location and stability of orbits, playing important role in black hole astrophysics. Generically, the equations are plagued by runaway solutions, so we discuss computational ways to avoid this problem in constructing numerical solutions. We calculate the corresponding energy and angular momentum loss of a particle and study the damping of charged particle oscillations around an equilibrium radius. We find that depending on the orientation of the Lorentz force, the oscillating charged particle either spirals down to the black hole, or stabilizes the circular orbit by decaying its oscillations. The latter case leads to an interesting new result of shifting of the radii of the particle orbit outwards from the black hole, but this shift is relatively slow. We also discuss the astrophysical relevance of the presented approach and provide estimations of the main parameters of the model.

**Author: **Vladimír Karas (Astronomical Institute of the Czech Academy of Sciences, Prague, Czech Republic)

**Title: ***Black Holes at Centenary of Einstein’s General Theory of Relativity: Testing the Nature of Black Hole Sources with X-rays*

Future observations will help us to test general relativity in the strong-field regime. No-hair theorem states states that stationary, isolated black holes can be fully characterized by a small number of parameters. However, cosmic black holes are not isolated; instead, they interact with their gaseous and stellar environment. We will discuss what "small number of parameters means" for astrophysically relevant objects in the era of forthcoming combined spectral, timing and polarimetric satellites.

**Author: **Michal Zajaček (University of Cologne, Germany; Max Planck Intstitute for Radio Astronomy, Bonn, Germany; Astronomical Institute of the Czech Academy of Sciences, Prague, Czech Republic)

**Co-authors: **A. Eckart, V. Karas, S. Britzen, et al.

**Title: ***Polarization properties of bow shock sources close to the Galactic centre*

Several bow shock sources were detected and resolved in the innermost parsec from the supermassive black hole in the Galactic centre. They show several distinct characteristics, including an excess towards mid-infrared wavelengths and a significant linear polarization as well as a characteristic prolonged bow-shock shape. These features give hints about the presence of a non-spherical dusty envelope generated by the bow shock. The Dusty S-cluster Object (also denoted as G2) shows similar characteristics and it is a candidate for the closest bow shock with a detected proper motion in the vicinity of Sgr A*, with the pericentre distance of only approx. 2000 Schwarzschild radii. However, in the continuum emission it is a point-like, unresolved source and therefore we use Monte Carlo radiative transfer modelling to reveal its three-dimensional structure. Alongside the spectral energy distribution, the detection of polarized continuum emission in the near-infrared Ks-band (2.2 mikrometers) puts additional constraints on the geometry of the source.

**Author: **Michal Bursa (Astronomical Institute of the Czech Academy of Sciences, Prague, Czech Republic)

**Title: ***Effects of geometry and mass accretion rate on thermal spectra of ULX sources*

Spectra of many ULX sources show a characteristic shape of double-peaked thermal spectra, where the first peak is most likely produced by true thermal contribution from the disk while the second peak probably comes from the thermal comptonization. The talk is going to show how the the observed shape of the thermal component is affected by geometrical setup of the system also in relation to the mass accretion rate and how the thermal spectrum changes as a result of thermal comptonization.

**Author: **Kostas Sapountzis (Center for Theoretical Physics – Polish Academy of Science)

**Title: ***Short Gamma Ray Bursts. The MRI print out on the launched jet – Time Variability*

In our current work we investigate the potential MRI imprint on an accreting Black Hole system resembling the one believed to apply in the Short Gamma Ray Bursts scenario. In such a phenomenon the emerging outflow is hyper-relativistic, of low baryon load and highly variable and although the precise radiation processes interfere are still ambiguous, the observed prompt light curve variability is associated with the hydrodynamic or magnetohydrodynamical properties of the outflow. From its point of view, MRI is the most prominent process that leads to the outward transportation of the angular momentum resulting to the plasma accretion. We developed a general relativistic model of ideal conducting plasma and we used HARM code to perform the corresponding simulation and to determine if a hyper-relativistic jet is launched and if the MRI maximum growth rate is reflected on the outflow.