### Scientific results obtained during the year 2016

The research has been continued in all the relevant regions stated in the project proposal, with attention focused to the astrophysical phenomena occurring around black holes and magnetic neutron stars and related spacetimes, treated within general relativistic approach or in the framework of alternative theories of gravitation.

**Optical and physical effects in alternate black holes and related spacetimes**

Based on the results of our research from previous year, we studied the accretion and optical effects in the regular black hole and no horizon Bardeen and Ayón-Beáto – García (ABG) spacetimes, namely of the spectral line profiles and the effect of `ghost image’ on the profiled line shape. As a reaction to the research of Ghasemi-Nodehi and Bambi, we studied the silhouette and spectral line profiles in special modification of Kerr geometry generated by quintessential field in order to demonstrate the influence of the quintessential field on specified optical phenomena.

*[J. Schee and Z. Stuchlík, Classical and Quantum Gravity, 33, 8, 2016]*

*[J. Schee and Z. Stuchlík, The European Physical Journal C, 76, 11, 2016]*

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We joined the new era of gravitational wave astronomy by the study of quasi-normal perturbative field modes of static braneworld black holes in the framework of Randall-Sundrum model to search for quantitative traces of the tidal charge in the braneworld black hole ringing. Continuing research of the properties of the braneworld compact objects, we gave the overview of the Keplerian accretion efficiency in the Kerr-Newman braneworld spacetimes. We have found a special extraordinary new class of the KN naked singularity spacetimes demonstrating the so called mining instability related to (formally) unlimited accretion efficiency.

*[B. Toshmatov, Z. Stuchlík, J. Schee, and B. Ahmedov, Physical Review D, 93, 12, 2016]*

*[M. Blaschke and Z. Stuchlík, Physical Review D, 94, 8, 2016]*

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We extended our studies also to rotating wormholes, focusing our investigation to their shadow created also under influence of plasma environment. We also introduced a new class of rotating black holes surrounded by quintessential energy field. We studied shadow of such quintessential black holes with inclusion of the plasma effects, and the particle collisions and related energy extraction and particle acceleration. The role of the plasma environment in the gravitational lensing by the regular black holes has been also investigated.

*[A. Abdujabbarov, B. Juraev, B. Ahmedov and Z. Stuchlík, Astrophysics and Space Science, 361, 226,2016]*

*[T. Oteev, A. Abdujabbarov, Z. Stuchlík and B. Ahmedov, Astrophysics and Space Science, 361, 269, 2016]*

*[A. Abdujabbarov, B. Toshmatov, Z. Stuchlík and B. Ahmedov, International Journal of Modern Physics D, 26, 1750051, 2017]*

*[A.Abdujabbarov, B.Toshmatov, J.Schee, Z.Stuchlík and B.Ahmedov, International Journal of Modern Physics D, 2017, in press]*

**Structures encircling compact objects**

We continued our investigation of dielectric charged toroidal structures of polytropic fluid. We focused on the structures centered in the equatorial plane, and also on those `levitating’ above equatorial plane of a compact object endowed with a dipole-type magnetic field. The main part of the work was represented by the topological study, showing up various classes of the tori (some of them exhibiting even three cusps, forming this way the so-called coupled rings). To contextualize the study we went through a physical discussion as well, fitting the pressure, density, charge and temperature profiles of the constructed tori so that they correspond to astrophysical limits. This work has been complemented by Newtonian study of the role of self-gravity on these charged fluid toroidal structures.

*[J. Kovář, P. Slaný, C. Cremaschini, Z. Stuchlík, V. Karas and A. Trova, Physical Review D, 93, 124055, 2016]*

*[A. Trova, V. Karas, P. Slaný and J. Kovář, The Astrophysical Journal Supplement Series, 226, 12, 2016] *

We continued our investigation of the so-called ringed accretion discs, i.e., complex multi-ring structures that could represent a remnant of several accretion regimes on a supermassive black hole. We analyzed the possibility that several instability points may be formed in the orbiting matter around a supermassive Kerr black hole in the ringed accretion disc model, proving that number of the instability points is limited and depends on the dimensionless spin of the rotating attractor.

*[D. Pugliese and Z. Stuchlík, Astrophysical Journal Supplement Series, 223, 2, 2016]*

**General relativistic polytropic configurations**

The effect of the repulsive cosmological constant on the possible relativistic polytropes was discussed and we demonstrated that the general relativistic polytropic configurations cannot exceed the static radius related to their external spacetime.

*[Z. Stuchlík, S. Hledík, and J. Novotný, Physical Review D, 94, 10, 2016] *

**Charged particles and string loops dynamics**

We studied the dynamics of the charged test particles in the vicinity of a black hole immersed into an asymptotically uniform magnetic field. We discussed the consequences of the model of ionization of test particles forming a neutral accretion disc and we explored the fate of charged test particles after ionization. We showed that a strong acceleration of the ionized particles to ultra-relativistic velocities is preferred in the direction close to the magnetic field lines, representing an alternative to the Blandford-Znajek process for creation of jets. We also explored circular orbits and related quasiharmonic oscillatory motion of charged particles around weakly magnetized rotating black hole. Different ratios of particle fundamental frequencies were used to explain different shapes of perturbed circular orbit.

*[Z. Stuchlík and M. Kološ, The European Physical Journal C, 76, 1, 2016]*

*[A. Tursunov, Z. Stuchlík and M. Kološ, Physical Review D, 93, 8, 2016]*

**Kinetic theory of collisional processes and variational principles in Kinetic Theory in GR.**

We continued the studies related to kinetic theory and its relation to both general relativity and quantum theory. We investigated the Hamilton structure of Schrodinger dynamic system, and generalized Lagrangian path representation of quantum mechanics. New approach to general relativity was studied being based on non-local point transformations. Kinetic theory of non-interacting particles has been studied for the Kerr spacetime in relation to the Carter constant of motion reflecting the hidden symmetry of the spacetime.

*[M. Tessarotto and C. Cremaschini, Advances in Mathematical Physics, 2016, 9619326, 2016]*

*[C. Cremaschini and M. Tessarotto, Applied Physics Research 8, 2, 2016]*

*[M. Tessarotto and C. Cremaschini, Foundations of Physics 46, 1022, 2016]*

*[C. Cremaschini and Z. Stuchlik, International Journal of Modern Physics D, 26, 1750001, 2017]*

**High frequency QPO’s in accretion discs around compact objects**

Frequencies of the three quasi-periodic oscillation modes observed simultaneously in the accreting black hole GRO J1655-40 were compared with the predictions of different theoretical models. The controversial estimates of the black hole mass M and the dimensionless spin a in the microquasar GRO J1655-40 implied by strong gravity effects related to the timing and spectral measurements were discussed. Such controversy can be cured if we abandon the assumption of the occurrence of the twin HF QPOs and the simultaneously observed LF QPO at a common radius.

*[Z. Stuchlík and M. Kološ, Astronomy & Astrophysics, 586, A130, 2016]*

*[Z. Stuchlík and M. Kološ, The Astrophysical Journal, 825, 1, 2016]*

Using the realistic neutron star equations of state, we studied the ways to constrain the models of twin peak quasi-periodic oscillations observed in the LMXB 4U 1653.

*[G. Török et.al, The Astrophysical Journal, 833, 273, 2016]*