### Scientific results

**Research in the year 2020**

In the year 2020, the Institute of Physics in Opava was established as part of the Silesian University in Opava, being on the level of faculties. The RCTPA is now part of the Institute of Physics. The research in RCTPA continued in all the opened branches, all the collaborations were developed very intensively. New active member of the RCTPA is dr. Mariia Churilova, who joined the research area oriented on physical properties of non-standard compact objects governed by alternative gravity theories.

Detailed information on the results published in impacted journals can be found in section Publications. Here we mention the most important results.

The research of RCTPA members continued in all the considered areas, but it was focused on two of them. The first one represents studies of the physical phenomena in the combined gravitational and electromagnetic fields in close vicinity of compact objects. In an extensive international collaboration, we substantially participated in the investigation of the importance of the electromagnetic interactions for the behavior of the hot spot observed due to the GRAVITY project in the Galaxy center near the source SgrA. Our results bring very important restrictions on the electric charge contained in both the central black hole and the hot spot (flare) (Tursunov et al., 2020, ApJ). Combining the results of our studies of the magnetic Penrose process and the results of the study of the acceleration of ionized particles due to the chaotic scattering in the field of magnetized Kerr black holes, we proposed a fundamentally new and simple mechanism for the acceleration of protons or ions in the field of magnetized supermassive black holes in active galactic nuclei that enables to explain the most energetic events observed in UHECRs, if physically realistic sufficiently large mass of the hole and intensity of the external magnetic field are available (Tursunov et al., 2020, ApJ). The proposed model of the particle acceleration is of the highest astrophysical relevance, because we are able to show that the radiation reaction of the accelerated protons or ions is negligible in the magnetic fields sufficient for such strong acceleration, contrary to the case of electrons that must be substantially decelerated in the same physical conditions. An extended summary of the gravomagnetic phenomena occurring around magnetized black holes for both charged particle dynamics, including the acceleration processes and the transitions between chaotic and regular motion, and properties of the dielectric charged fluid configurations, both equatorial and off-equatorial, was presented in (Stuchlik et al., 2020, Universe).

We found fundamentally new radiative Penrose process that enables extraction of the rotational energy of the magnetized Kerr black holes due to the synchrotron radiation of charged particles in the black hole ergosphere – this effect is caused by radiation of photons with negative energy as related to distant observers (Kolos et al., 2020, arxiv).

The model of dielectric charged fluid tori was introduced in terms of two kinds of covariant forces, with behavior reflected in the related conformal geometries. Such force description of the circulating non-conducting charged fluid structures represents a very useful tool for further studies of these astrophysically very important objects (Kovar et al., 2020, CQG). The standard approach was applied to the study of dielectric tori in the field of electrically charged black hole immersed in an external uniform magnetic field (Trova et al., 2020, PRD).

The second extensively surveyed area was related to the properties of exotic compact objects governed by alternative gravity theories, including the multi-dimensional ones. General parameterization of higher-dimensional black holes and its application to the Einstein-Lovelock theory gives relevant information on a possibility to write down black hole spacetimes with many coupling constants in a compact analytic form (Konoplya et al., 2020a, PRD). Properties of the black holes in the Lovelock theory were considered extensively in (Konoplya and Zhidenko, 2020, PRD). Quasinormal modes and Hawking radiation of black holes in qubic gravity were studied in (Konoplya et al., 2020b, PRD). Transition of the regular black holes to wormholes and aspects of ringing of these objects during the transition were discussed in (Churilova and Stuchlik, 2020, CQG). Large attention was devoted to the Gauss-Bonnet black holes. The regular 5D Gauss-Bonnet black holes with non-linear electrodynamics were studied in (Churilova and Stuchlik, 2020, AnPhys). Special focus was devoted to the slightly controversial case of the 4D Gauss-Bonnet black holes. Motion of charged particles with focus on the properties of the epicyclic motion in the 4D Einstein-Gauss-Bonnet black holes immersed in an external magnetic field was studied in (Shaymatov et al., 2020, PDU). Quasinormal modes of the 4D Gauss-Bonnet black holes were treated in (Konoplya et al., 2020, PRD). Stability of the black holes in 4D Einstein-Gauss-Bonnet gravity and Einstein-Lovelock gravities was studied in (Konoplya and Zhidenko, 2020, PDU), and the grey-body factor and Hawking radiation in the 4D Einstein-Gauss-Bonner black hole spacetimes were discussed in (Konoplya and Zinhailo, 2020, PLB).

Motion of charged and magnetized particles in the field of generic singular black holes in GR coupled with non-linear electrodynamics was studied in (Vrba et al., 2020, PRD). Epicyclic motion in the field of Kerr-MOG black holes and its relation to the HF QPOs observed in microquasars were investigated in (Kolos et al., 2020, EPJC). Stability of circular geodesics of the Kerr-Newman-de Sitter black hole and naked singularity spacetimes was presented in (Slany and Stuchlik, 2020, EPJC).

The ringed accretion disks were studied for the fundamentally new case of misaligned tori that can represent a complex surrounding of a central black hole with equatorial accretion disk, as can be observed in many galaxies and their nuclei regions (Pugliese and Stuchlik, 2020, CQG). Relation of the ringed accretion disks to oscillatory states of their toroidal components was discussed in (Pugliese and Stuchlik, 2020, MNRAS).

Stability of the polytropic spheres was studied in (Hladik et al., 2020, IJMPD) -- the equilibrium and the dynamic methods were compared and some small differences were commented. The much more interesting detailed study of the stability of the polytropic spheres in the spacetimes with the cosmological constant against the radial pulsations was presented in (Posada et al., 2020, EPJC). The differences of the equilibrium and dynamic methods increase with increasing cosmological parameter given by the ratio of the vacuum energy density (cosmological constant) and the central density of the polytrope matter.

Another fundamental work was related to the trapping of null geodesics in extremely compact objects under assumption of small rotation – although we used the simplest model of the internal Schwarzschild spacetime, treating the rotational effects in the first order of the angular velocity of the object, it brought an important general result of strong overcoming of the trapping of counterrotating null geodesics in comparison to the corotating ones (Vrba et al., 2020, EPJC).

Studies of chaos and regularity in astrophysics were continued in two directions. On the purely theoretical ground, the time series of the particle motion in spacetimes of magnetized black holes were studied, using the non-linear methods for the case of magnetized Kerr holes. On the observational grounds, we started in collaboration with dr. Gopal Bhatta from the Krakow University studies of the detectability of deterministic character of physical processes, using the non-linear methods for analysis of the observational data obtained from blazars – signatures of deterministic processes in the light curves of many blazars were detected in (Bhatta et al., 2020, ApJ).The research on both theoretical and observational aspects of chaos and regularity and their relations will be extended due to the contributions of dr. Karel Adamek and dr. Jan Novotny, who returned from postdoc stays at Oxford University.

**Research in the year 2019**

The research continued in all the branches, being substantially extended. Thanks to the collaboration with colleagues from the Koln University and MPI Bonn, the phenomena observed by the GRAVITY experiment were studied in the direction related to restrictions on the electromagnetic interactions between charged matter and charged black hole in the Galaxy center. Another collaborations started for the modelling of accretion disk in the magneto-hydrodynamic approach, with the Harvard University and the Warsaw University. Fundamental extension of the research areas was devoted to the studies relating chaos and regularity. RCTPA was supported by the Czech Science Foundation in the standard project No. 19-03950S, granted for the period 2019-2021. Withis this project RCTPA was joined by dr. Thomas Pappas. Finally, we have to mention that RCTPA was established as a part of ICRANET -- the collaboration is assumed mainly in the region of gravomagnetic phenomena around compact objects.

Detailed information on the results published in impacted journals can be found in this file. Here we mention the most important results.

Relevant limits on the charge of the magnetized black hole located in the Galactic center (SgrA) were obtained in (Zajacek et al., 2019, MNRAS). Extensive studies of various aspects of the dynamics of charged matter (ionized Keplerian disks) were started in relation to both the oscillatory phenomena in vicinity of the black hole horizon, and the acceleration of the ultra-high energy cosmic rays (UHECRs).

Energetics of the ringed accretion disks and restrictions on the collisions of tori around supermassive Kerr black holes were treated in (Pugliese and Stuchlik, 2019, EPJC). In collaboration with the Black Hole Initiative center at the Harvard University, for modelling time-dependent accretion disks of different thickness, a model of the socalled puffy accretion disks was developed (Lancova et al., 2019, ApJL).

We started a series of works related to the proper description of the optical effects in the field of the regular black holes governed by GR combined with the non-linear electrodynamics, as the photon dynamics is no longer governed by the spacetime geometry, but by an effective geometry directly reflecting the influence of the non-linear character of the electrodynamic phenomena. The effective geometry was introduced and its influence on the shadow of the regular black holes was studied in (Stuchlik and Schee, 2019, EPJC), while the frequency mapping of the Keplerian was treated in (Schee and Stuchlik, 2019, ApJ). In both cases, it was shown that the regular black holes are acceptable from the observational point of view only for the versions of the non-linear electrodynamics having the proper Maxwell weak field limit – a wrong limit of the behavior of the black hole shadow for vanishing charge was demonstrated for the non-linear electrodynamic theories having non-Maxwelian weak field limit also in (Toshmatov et al., 2019, PRD). For this reason, a detailed study of Keplerian disk and their appearance was performed only in the case of generic regular black holes having the Maxwell weak field limit (Stuchlik et al., 2019, ApJ). Particle motion in the field of the generic regular black holes related to the non-linear electrodynamics was discussed in (Vrba et al., 2019, EPJC).

An interesting study of the influence of a hidden dark matter located in close vicinity of a black hole horizon onto the shadow of the black hole was presented in (Konoplya, 2019, PLB) -- it was demonstrated that strong effects can occur only in the case of the mass concentrated extremely close to the horizon.

The method of minimal geometrical deformation was used in combination with the gravitational decoupling in several studies related to various compact objects, e.g. for generalization of the Tolman VII solution to anisotropic case (Hensh and Stuchlik, 2019, EPJC). Important seem to be the study of the isotropization and change of complexity of anisotropic solutions by gravitational decoupling (Casadio et al., 2019, EPJC), or the study of anisotropic ultracompact Schwarzschild stars that could be interesting in relation to the models of gravastars (Ovalle et al., 2019, CQG). A very relevant summary concerning the method of the gravitational decoupling was presented in (Ovalle, 2019, PLB).

The relation of the chaos and regularity was treated in the theoretical study devoted to finding of chaotic behavior in time series generated by the model of charged particle motion of ionized Keplerian disk in the field of magnetized Schwarzschild black hole – the regions of chaos and islands of regularity can be clearly determined by using the non-linear methods of treating the time series, and efficiency of the machine learning methods was clearly demonstrated (Panis et al., 2019, EPJC). From the physical point of view, it is important that the chaotic character of the motion increases with increasing inclination angle between the disk and the magnetic field lines.

For the theory of HF QPOs, the study of the properties of the radial profiles of the epicyclic and orbital frequencies related to the circular geodesics in the vicinity of the neutron stars represented by the external Hartle-Thorne geometry containing the three parameters, representing mass, spin and quadrupole momentum, seems to be very important (Urbancova et al., 2019, ApJ). It is crucial that the results clearly demonstrate correctness of applicability of the Kerr geometry instead of the external Hartle-Thorne geometry only for values of the dimensionless reduced quadrupole moment very close to the Kerr value. We also applied the epicyclic geodesic model of HF QPOs, as related to the systems containing a black hole, to the exceptional extragalactic X-ray source XMMUJ134736.6+173403, obtaining important limits on the range of mass of the black hole assumed in the center of this source (Goluchova et al., 2019, AA).

Studies of the quasinormal modes of test fields around black holes in alternative gravity theories were performed in the case of Einstein-dilaton-Gauss-Bonnet theory, taking into account also the Hawking radiation of such black holes (Konoplay et al., 2019, PRD). Echoes of the compact objects, influenced by surrounding matter, were treated in (Konoplya, 2019, PRD). Possibility to have stable Schwarzschild stars as black hole mimickers was considered in (Konoplya et al., 2019, PRD).

Studies of the cosmological models were concentrated on the possibility to explain the observed accelerated expansion of the Universe in the framework of inhomogeneous models of the Universe, the relevant conditions and restrictions were given in (Kopteva et al., 2019, ApJ).

**Research in the year 2018**

The research continued in all the opened branches, being substantially extended to new directions. Detailed information on the results published in impacted journals can be found in this file. Here we mention the most important results.

One of the new directions of the RCTPA research is related to application of the method of minimal geometric deformation in combination with gravitational decoupling that was developed by dr. Jorge Ovalle, who joined RCTPA in 2018. We found interesting black hole solutions by the gravitational decoupling that enables to precisely treat influence of dark matter on known black hole solutions (Ovalle et al., 2018, EPJC).

The other new direction of research is related to the magnetic Penrose process, started in collaboration with prof. Naresh Dadhich from the Pune University, and related issue of radiative reaction on the motion of charged particles in the field of magnetized black holes, started in collaboration with prof. Dmitriy Galtsov from the Moscow University. During our study of the distinguishing signature of the magnetic Penrose process we arrived to a very interesting classification of the magnetic Penrose process and demonstration of the fact that the Blandford-Znajek process can be considered as a special kind of the magnetic Penrose process (Dadhich et al., 2018, MNRAS). In the study of the radiation reaction of charged particles orbiting a magnetized Schwarzschild black hole we demonstrated that in astrophysically plausible situations this phenomenon is crucial in the case of friction of the electron motion, but it is strongly suppressed for motion of protons and heavy ions (Tursunov et al., 2018, ApJ). Moreover, there is an unexpected phenomenon of widening of circular orbits due to the radiation friction, acting on long time scales (Tursunov et al., 2018, AN). The combination of the magnetic Penrose process and the radiation reaction of the charged particle motion is expected to be a very promising approach to understand the most energetic phenomena observed in active galactic nuclei, or in microquasars, and to describe the processes in the field of magnetic neutron stars, especially in the case of magnetars with extremely intensive magnetic fields.

The ringed accretion disks were studied in situations relevant in astrophysics, namely they were considered as remnants of various accretion phases in the galactic centers (Pugliese and Stuchlik, 2018, JHEA), and treated as structures surrounding supermassive Kerr black holes in the active galactic nuclei (Pugliese and Stuchlik, 2018a, CQG). Alternatively, the proto jet structures were considered as a relevant part of the ringed accretion phenomena (Pugliese and Stuchlik, 2018b, CQG).

In collaboration with colleagues from the Bremen University, our investigation of the dielectric charged tori was extended to both equatorial and off-equatorial tori orbiting a magnetized Kerr black hole (Trova et al., 2018, PRD).

The dynamics of charged string loops in the field of Reissner-Nordström black holes was treated, and possible enrichment of the modelling of the QPO phenomena in the black hole systems was presented in (Oteev et al., 2018, EPJC).

We performed a detailed study of the escape (trapped) light cones of photons (and related black hole shadows) in the field of Kerr-de Sitter black holes, considering the locally non-rotating frames, the frames of observers related to circular geodesics, and frames related to radially falling or escaping observers that are very relevant in the asymptotically de Sitter spacetimes – inside the trapping cones very important part of photons with negative energy is determined for sources moving in the ergosphere (Stuchlik et al., 2018, EPJC). The special case of spherical photon orbits and their nodal shifts is discussed in (Charbulak and Stuchlik, 2018, EPJC).

The electromagnetic perturbations in the field of black holes described by GR combined with the fractional non-linear electrodynamics were treated both for axial case (Toshmatov et al., 2018a, PRD) and polar perturbations (Toshmatov et al., 2018b, PRD).

The exacts cosmological solutions describing a black hole immersed in a non-static inhomogeneous universe was studied, and correctly defined black hole horizons were introduced in (Kopteva et al., 2018, ApJ).

Long-lived quasinormal modes and instabilities of the non-minimally coupled scalar fields in the Reissner-Nordström backgrounds were studied in (Konoplya et al., 2018, PRD). Another studies on the quasinormal modes gave us also interesting results, namely in the case of general wormholes (Konoplya, 2018, PLB), or wormholes in the Einstein-dilaton-Gauss-Bonnet theory (Cuyubamba et al., 2018, PRD).

**Research in the year 2017**

The research continued in all the opened branches successfully, moreover, it was substantially extended to two new directions. Detailed information on the results published in impacted journals can be found in this file. Here we mention the most important results.

In collaboration with dr. Elena Kopteva from Dnepropetrovsk University, RCTPA started investigations in the field of cosmology, namely inhomogeneous cosmological models allowing for description of cosmological black holes (Kopteva et al., 2017, GRG). Even more important is opening of the studies of multidimensional black holes governed by various alternatives to the Einstein gravity, in collaboration with dr. Roman Konoplya from the Tubingen University, who joined RCTPA. In this case we obtained a fundamentally new result -- a counterexample to the close relations between the black hole quasinormal modes in the eikonal approximation and the Lyapunov coefficient of its unstable circular null geodesics (Konoplya and Stuchlik, 2017, PLB).

The study of the properties of the mining Kerr-Newman naked singularities led to very interesting results. We demonstrated that the Banados-Silk-White process of ultra-high energy collisions can be very efficient in the case of such spacetimes, moreover, we were able to show that such a spacetime can be an efficient source of energy for a civilization orbiting in its close vicinity, enabling thus its survival in far future eras of the existence of the Universe (Stuchlik et al., 2017, PRD).

Very interesting phenomena were demonstrated in the case of extremely compact polytropes. First, it was shown that the extremely compact polytropes can exist starting at the value of polytropic index n=2.2, corresponding to realistic equations of state from the viewpoint of standard microphysics. Moreover, the compactness of the extremely compact region containing null geodesics was shown to be smaller than those of the internal Schwarzschild spacetimes (Novotny et al., 2017, PRD). Second, the special class of the extremely compact polytropes with extremely large total extension, comparable with extension of large galaxies or their clusters, have gravitationally unstable internal extremely compact region that should undergo gravitational collapse. Therefore, in the framework of the dark matter halo model based on extended polytropes, a supermassive black hole can be created in the center of halos related to large galaxies (Stuchlik et al., 2017, JCAP). We thus constructed an alternative model for creation of supermassive black hole in the high redshift eras of the Universe evolution.

In the research area of interpretation of the HF QPOs and their fitting by the geodesic epicyclic oscillation model, we realized fitting of the data observed in microquasars assuming a central Kerr superspinar instead of a black hole – in this case there exist some variants of the geodesic model enabling fitting of the data in all the considered microquasars, contrary to the case where a central black hole is assumed (Kotrlova et al., 2017, AA). Special predictions for fitting the data in atoll sources containing a neutron star or a quark star were tested for the case of superspinning quark stars, with the dimensionless spin overcoming the extreme Kerr black hole limit, that could be so fast spinning due to contribution of the strong forces acting in binding of the star in addition to gravity (Stuchlik et al., 2017, AcA).

Of high astrophysical relevance are the results of the study of the epicyclic geodesic model of the HF QPOs modified by the electromagnetic interaction of the electrically charged, ionized matter in the Keplerian disks with slightly magnetized Kerr black holes (Kolos et al., 2017, EPJC). Of high interest are also results of the study of the ringed accretion disks related to interactions of the corotating and counterrotating tori representing neighbor parts of such disks (Pugliese and Stuchlik, 2017, ApJS).

We found a new rotating black hole solution generalizing the Kiselev quintessential black hole (Toshmatov et al.017a, EPJP) and studied the astrophysical consequences of the particle motion in the field of rotating quintessential black holes, demonstrating very important existence of the so- called static radius, where the repulsive force of the quintessence is just balanced by the black hole attraction. The shadow of such a black hole immersed in plasma was described in (Abdujabbarov et al., 2017, IJMPD). Another interesting family of rotating solutions was constructed in the case of generic regular black holes within a special class of fractional non-linear electrodynamics (Toshmatov et al., 2017, PRD).

Studies of perturbative field quasinormal modes of black holes in alternative gravity theories were started, namely in the case of the black holes governed by the conformal gravity (Toshmatov et al., 2017, PRD). Interesting phenomena were discovered also in the case of slowly decaying resonances of massive scalar field in the Schwarzschild-de Sitter black hole backgrounds, where the static radius plays a crucial role (Toshmatov and Stuchlik, 2017b, EPJP).

Of special interest is an extraordinary effect of classical corrections of entropy of d-dimensional black holes that could serve as a rare window to quantum gravity (Blaschke et al., 2017, PRD).

**Research in the year 2016**

The research in all three areas developed in the period 2013-2015, participation in the LOFT project, and collaboration with foreign colleagues on common projects, were successfully continued. In 2016 RCTPA was supported by the Czech Science Foundation by the Junior project No. 16 – 03564Y, granted for the period 2016-2018. We introduced a new modification of the studies of optical phenomena, taking into account plasma located in vicinity of black holes or alternative compact objects.

Complete list of results presented in impacted journals in this period can be found in this file. Here we mention some of the most interesting results.

As the most important from the view point of astrophysics, we point out our studies of ionized Keplerian disks orbiting a magnetized Kerr black hole with asymptotically uniform external magnetic field. We demonstrated possibility of strong acceleration of the ionized matter due to the effect of chaotic scattering – after ionization, originally neutral orbiting matter undergoes a short period of chaotic motion and finally escapes to infinity along the magnetic field lines in the ultrarelativistic regime, if the electromagnetic interaction is strong enough (Stuchlik and Kolos, 2016, EPJC). On the other hand, the ionized matter can be transformed into epicyclic oscillatory motion, if the electromagnetic interaction is low enough – circular orbits of charged matter and the frequencies of the oscillatory motion are presented in (Tursunov et al., 2016, PRD).

Models of HF QPOs, both the epicyclic geodesic models and the string loop oscillatory models were applied to explain some difficulties of fitting the data from some microquasars (Stuchlik and Kolos, 2016, ApJ). Restrictions on applicability of the resonant models of twin HF QPOs in systems containing a neutron star were realized by using realistic equations of state in fitting the observational data (Torok et al., 2016, ApJ).

The study of equilibrium equatorial ringed disks orbiting Kerr black holes was extended for discussion of the instabilities of the ringed disks related to the accretion processes and possible collisions of the corotating and counterrotating tori constituting a ringed disk (Pugliese and Stuchlik, 2016, ApJS). Existence of off-equatorial dielectric charged toroidal configurations was demonstrated for spherical gravitational fields combined with dipole magnetic field in (Kovar et al., 2016, PRD), the dielectric tori with an inclusion of self-gravity effects were treated in (Trova et al., 2016, ApJS).

A new direction of investigations was opened being related to the non-vacuum spherically symmetric solutions of the Einstein gravitational equations with matter under realistic or artificial equations of state. The study was now focused on the polytropes in spacetimes including the cosmological constant. Several very important results were found – we particularly stress the restriction on extension of the polytropes given by the parameter combining the cosmological constant and mass of the configuration, and existence of extremely compact small central regions located inside extremely extended polytropes with diameter comparable to those of large galaxies or even galaxy clusters (Stuchlik et al., 2016, PRD).

Fundamentally new and very interesting results were obtained for Keplerian accretion disks orbiting in the Kerr-Newman spacetimes of both black hole and naked singularity type, with inclusion of the braneworld Ker-Newman spacetimes where the tidal charge can take also negative values, in contrast to the standard GR case. The classification of the Kerr-Newman spacetimes was given, being based on the character of the geodesic motion. Surprisingly, we found a special type of the spacetime that was overlooked for all the years of black hole physics development -- the so-called mining Kerr-Newman naked singularity spacetimes where the efficiency of the Keplerian accretion can (of course formally) tend to infinity, having thus extraordinary astrophysical consequences, leading for example to possibility of almost complete extraction of the gravitational mass of the mining Kerr-Newman naked singularities (Blaschke and Stuchlik, 2016, PRD).

**Research in the period 2013 – 2015**

In the introductory period of existence of the Research Centre for Theoretical Physics and Astrophysics (RCTPA), the research was concentrated on astrophysical processes in vicinity of black holes, or alternatively superspinars, and neutron or quark stars, governed by the standard Einstein theory of gravity, i.e., general theory of relativity (GR), or some alternative theories of gravity. Predictions of the relativistic astrophysics models were frequently applied to explain observational data from microquasars or some atoll sources containing a neutron star, and to estimate parameters of these compact objects. In 2014, RCPTA started its participation in the Albert Einstein Center for Gravitation and Astrophysics supported by the Czech Science Foundation by the excellence project No. 14-37086G, granted for the period 2014-2018. Internationalization of RCTPA started during the period 2013-2015 -- Dr. Daniela Pugliese joined RCTPA in 2014, and extensive cooperation with the relativistic group at the Tashkent University was initiated, extending thus the previous collaborations with colleagues from Oxford University, CAMK Warsaw, ISAS Trieste, etc.

The research was performed in several important and extensive areas. Complete list of results presented in impacted journals can be found in files 2015, 2014, 2013. Here we mention some of the most interesting results.

__Accretion structures around black holes, superspinars or neutron stars__

The accretion structures, both toroidal and Keplerian disks, were treated by various methods: using the test particle approach governing the Keplerian disks, the kinetic approach for description of plasmatic structures, and fluid description that has been applied in the case of complex, equatorially centred structures orbiting Kerr black holes, i.e. ringed disks composed generally from both corotating and counterrotating tori (Pugliese and Stuchlik, 2015, ApJS).

The most interesting appears research of charged fluid structures around magnetized black holes (or neutron stars) treated in the “dielectric” approximation of zero conductivity that can be considered as complementary with respect to well established “force free” approximation corresponding to infinite conductivity (Kovar et al., 2014, PRD). Of great astrophysical relevance are also studies of the charged particle motion around magnetized black holes (Kolos et al., 2015, CQG).

Properties of magnetized tori with toroidal fields orbiting Kerr superspinars were presented in (Adamek and Stuchlik, 2015, CQG). It was also shown that strongly ultra-high energy photons generated by the Banados-Silk-White collisions can be detected by distant observers, if realized in the field of Kerr superspinars (Stuchlik and Schee, 2013, CQG), contrary to the case of black holes.

Toroidal fluid structures around Kehagias-Sfetsos black holes of the Hořava-Lifshitz quantum gravity were constructed in (Stuchlik et al., 2015, EPJC), while their astrophysical properties were treated in (Toshmatov et al., 2015, ASS).

It was shown in a series of papers that the kinetic approach can bring interesting information on the properties of collisionless plasmas around black holes -- the most important result demonstrates possibility to create magnetic loops by gravitationally bound plasmas (Cremaschini and Stuchlik, 2013, PRE).

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__Models of oscillations of accretion disks and their relation to HF QPOs in microquasars and atoll sources__

One of the most promising explanations of the high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars, i.e. binary systems containing a black hole, or binary systems containing a neutron (quark) star, are related to assumed resonant phenomena that could occur between oscillatory models of accretion disks. We constructed a general multi-resonance orbital model of HF QPOs based on frequencies of the epicyclic geodesic motion that in principle enables high-precision determination of black hole or neutron star dimensionless spin parameter (Stuchlik et al., 2013, AA).

As an interesting application we proposed the so-called resonant-switch model enabling precise explanation of data in some atoll sources containing neutron stars (Stuchlik et al., 2014, AcA). Parameters of these neutron stars can be then rather precisely determined using the Hartle-Thorne theory. Parameters of the external Hartle-Thorne geometry are the mass, dimensionless spin and dimensionless reduced quadrupole moment – they can be precisely calculated for given equation of state of the neutron star on one side, and can be well restricted by the observational data on the other side. Astrophysics can thus give strong restrictions on the particle microphysics governing the equation of state. Moreover, we demonstrated that the most massive neutron stars allowed by a given equation of state are most compact and have their reduced quadrupole moment very close to the Kerr limit when the Kerr geometry can be good approximation of the neutron star external spacetime (Urbanec et al., 2013, MNRAS). These results were confirmed by precise fitting of the HF QPO data from some atoll sources to the resonant switch model (Stuchlik et al., 2015, AcA, Stuchlik and Kolos, 2015, GRG). The resonant models of HF QPOs were also applied to explain microquasar data – it was shown that all the microquasar data can be explained by an unique variant of the resonant models only under assumption of a central Kerr superspinar (Kotrlova et al., 2014, AA).

A plausible alternative to the resonant models based on frequencies of epicyclic geodesic oscillations is represented by application of the model of oscillating string loops with their tension parameter enabling precise fitting of the observational data (Stuchlik and Kolos, 2015, MNRAS). We introduced a generalized concept of electrically charged strings (Tursunov et al., 2014, PRD) that can be relevant around magnetized black holes. Another interesting possibility is related to oscillations of charged test particles in the field of magnetized black holes (Kolos et al., 2015, CQG).

The research related to models of the HF QPOs due to oscillating accretion disks represents an important contribution to preparation of cosmic X-ray observatories, namely to the project LOFT.

__Regular black holes and their astrophysics__

Special kind of the RCTPA research is represented by modeling of black hole spacetimes resulting from combination of GR with various variants of non-linear electrodynamics that predicts the so- called regular black hole spacetimes having no physical singularity, and their counter parts called no-horizon strong gravity spacetimes corresponding to naked singularity spacetimes in standard GR metrics. We constructed rotating regular black hole spacetimes from the spherically symmetric ones (Toshmatov et al., 2014, PRD) and studied behavior of perturbative fields on the background of regular black holes. Particle motion around rotating regular black holes was treated in (Toshmatov et al., 2015, ASS). We further studied the particle and photon motion in the regular black hole and no-horizon spherically symmetric spacetimes, demonstrating a shift from de Sitter to anti de Sitter character of the central region of these spacetimes, if the charge parameter crosses a particular limiting value (Stuchlik and Schee, 2015, IJMPD). Moreover, in the case of the no-horizon spacetimes, we demonstrated a new optical effect corresponding to the existence of additional “ghost” images of orbiting structures (Schee and Stuchlik, 2015, JCAP). The quasinormal modes of test fields around spherically symmetric regular black holes were studied in (Toshmatov et al., 2015, PRD) – suppression of the damping of the quasinormal modes with increasing charge parameter was demonstrated.