**ABSTRACTS**

**Author: **Ahmedov Bobomurat (Uzbekistan Academy of Sciences, Uzbekistan)

**Title: ***Optical properties of axially symmetric black holes*

The shadow of a rotating (i) non‐Kerr, (ii) Horava‐Lifshitz, (iii) Kerr‐Taub‐NUT, (iv) five‐dimensional rotating Myers‐Perry and other black holes in vacuum has been studied, and it was shown that in addition to the specific angular momentum a, (i) the deformation parameter of non‐Kerr spacetime, (ii) parameters of Horava‐Lifshitz spacetime, (iii) nonvanishing gravitomagnetic charge, and other parameters essentially deform the shape of the black hole shadow. A comparison of the obtained theoretical results on the polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the dimensionless deformation parameter as 19, the upper limit for the Horava‐Lifshi tz δ parameter as δ ≤ 2.1∙10 ‐3 etc. Then gravitational lensing in the vicinity of a slowly rotating massive object surrounded by plasma has been studied. The obtained deflection angle of the light ray in the presence of plasma depends on (i) the frequency of the electromagnetic wave, due to the dispersion properties of the plasma; (ii) the gravitational mass M; and (iii) the angular momentum J=aM of the gravitational lens. We have studied photon motion around axially symmetric rotating (i) Kerr black hole, (ii) wormhole in the presence of a plasma with radial power‐law density. It is shown that in the presence of a plasma, the observed shape and size of the shadow of rotating (i) Kerr black hole, (ii) wormhole changes depending on the (i) plasma parameters, (ii) gravitational object spin, and (iii) inclination angle between the observer plane and the axis of rotation of the black hole/wormhole. Finally, we have developed a general formalism to describe the black hole shadow as an arbitrary polar curve expressed in terms of a Legendre expansion. New dev eloped formalism does not presume any knowledge of the properties of the shadow, e.g., the location of its center, and offers a number of routes to characterize the distortions of the curve with respect to reference circles. These distortions can be implemented in a coordinate independent manner by differ ent teams analyzing the same data. It has been shown that the new formalism provides an accurate and robust description of noisy observational data, with smaller error variances when compared to previous measurements of the distortion.

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

**Title: **

*Studying the space-time near the black hole embedded into cosmological dust*

We present the model of the Schwarzschild-like neutral black hole embedded into dust cosmological background for the flat space case based on the exact solution of Einstein equations in comoving coordinates. We investigate the resulting space-time of the model studying the motion of test particle near the black hole using geodesic equations. Observable velocity of the particle moving relatively to the observer comoving with cosmological expansion is found. In frame of the model it turns out that the total velocity of the particle tends to zero with time. It means that the particle will be involved to the cosmological expansion in case it was not travelling towards the center, otherwise it would fall into the singularity.

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

**Co-authors: **Zajaček Michal, Eckart Andreas, Kunneriath Devaky, Sabha Nadeen, Shahzamanian Banafsheh, Štofanova Lýdia, Valencia-Schneider Monica

**Title: **

*Modelling the bow-shock evolution along the DSO/G2 orbit in the Galactic centre*

A radially directed flow of gaseous environment from a supermassive black hole affects the evolution of a bow-shock that develops along the orbit of an object passing through the pericenter. The bow-shock exhibits asymmetry between the approaching and receding phases, as can be seen in calculations of the bow-shock size, the velocity profile along the shocked layer, and the surface density of the bow-shock, and by emission-measure maps. We discuss these effects in the context of the recent pericenter transit of DSO/G2 near Sagittarius A*.

**Author: **Kopteva Elena (Dniepropetrovsk National University, Ukraine)

**Title: **

*New exact solutions for Schwarzschild-like black holes*

We use the so called mass function method for obtaining new exact solutions for Schwarzschild-like black holes. The mass function is one of four algebraic invariants for general spherically symmetric metric. Rewriting Einstein equations in terms of mass function we consider Schwarzschild-like black holes. We show that Schwarzschild black holes should necessarily contain non-baryonic matter. We furthermore obtain new exact solutions for the black hole embedded into the dust matter universe.

**Author: **Miller John (University of Oxford, UK; SISSA, Italy)

**Title: ***The behaviour of trapping horizons during black hole formation*

Following the seminal work of Hayward (1994) there has been a growing interest in the behaviour of marginally trapped surfaces (known as trapping horizons) within matter collapsing to form black holes. Some of these surfaces can go on to become event horizons while others disappear into the interior of the matter and may be connected with the process of singularity avoidance in the quantum regime. The terminology used when discussing them varies from author to author and can be quite opaque to outsiders. We have developed a new way for talking about them which we think is more transparent and which has led to some new insights. This talk will present a progress report on our work.

**Author: **Pérez Daniela (University of La Plata, Argentina)

**Co-authors: **Romero Gustavo

**Title: **

*Accretion in modified gravity*

Stellar-mass black holes offer what is perhaps the best scenario to test theories of gravity in the strong-field regime. In particular, f(R) theories, which have been widely discuss in cosmological contexts, can be constrained through realistic astrophysical models of phenomena around black holes. We present here radiative models of thin accretion disks for both Schwarzschild and Kerr black holes in f(R)-gravity. We calculate the spectral energy distribution of the accretion disk around constant Ricci scalar f(R) black holes (equivalent to SdS spacetimes), and constrain specific f(R) prescriptions using observational features of actual systems. We conclude that a precise determination of both the spin and accretion rate onto black holes along with X-ray observations of their thermal spectrum might allow to identify deviations of gravity from general relativity. The case of thick accretion disks (tori) is briefly discussed.

**Author: **Pugliese Daniela (Silesian University in Opava, Czech Republic)

**Co-authors: **Stuchlík Zdeněk

**Title: **

*Ringed accretion disks: equilibrium configurations*

We investigate a model of ringed accretion disk, made up by several rings rotating around a supermassive Kerr black hole attractor. Each toroid of the ringed disk is governed by the General Relativity hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. Properties of the tori can be then determined by an appropriately defined effective potential reflecting the background Kerr geometry and the centrifugal effects. The ringed disks could be created in various regimes during the evolution of matter configurations around supermassive black holes. Therefore, both corotating and counterrotating rings have to be considered as being a constituent of the ringed disk. We provide constraints on the model parameters for the existence and stability of various ringed configurations and discuss occurrence of accretion onto the Kerr black hole and possible launching of jets from the ringed disk. We demonstrate that various ringed disks can be characterized by a maximum number of rings. We present also a perturbation analysis based on evolution of the oscillating components of the ringed disk. The dynamics of the unstable phases of the ringed disk evolution seems to be promising in relation to high energy phenomena demonstrated in active galactic nuclei.