The motion of a test particle in the Schwarzschild background models the merger of a compact object binary with extremely different masses known in the literature as Extreme Mass Ratio Inspiral. In the simplest geodesic approxima- tion, this motion is integrable and there is no chaos. When one takes the spin of the smaller body into account, integrability is broken and prolonged resonances along with chaotic orbits appear. By employing the methods of Poincaré surface of section, rotation number and recurrence analysis we show for the first time that there is chaos for astrophysically relevant spin values. We propose a uni- versal method of measuring widths of resonances in perturbations of geodesic motion in the Schwarzschild spacetime using action-angle-like variables. We ap- ply this novel method to demonstrate that one of the most prominent resonances is driven by second order in spin terms by studying its growth, supporting the expectation that chaos will not play a dominant role in Extreme Mass Ratio Inspirals. Last but not least, we compute gravitational waveforms in the time- domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source. 1

In this thesis we study exact general relativistic space-times generated by a black hole and an additional source of gravity, while restricting to two classes of static and axially symmetric solutions: the Majumdar-Papapetrou solution for a couple (in general, a multiple system) of extremally charged black holes and the "superposition" of a Schwarzschild black hole with the Bach-Weyl thin ring. We follow the effect of the additional source on the geometry of black-hole space-time on the behaviour of important invariants, in particular of the simplest scalars obtained from the Riemann and possibly also Ricci tensor. We have plotted the invariants both outside and inside the black hole; in the case of a Schwarzschild black hole with ring, we found, to this end, an extension of the metric below the horizon. It turns out that the external source may affect the geometry inside the black hole considerably, even in the vicinity of singularity, although the singularity itself remains point-like in both solutions studied here.

Black hole spin is an essential parameter, for it provides us with the infor- mation on the black hole formation and growth. In this Thesis, we simulated observations for an upcoming X-ray polarimetric mission IXPE (Imaging X- ray Polarimetry Explorer) with the aim to study the robustness of black hole spin and inclination measured via X-ray polarimetry. To simulate polarization spectra, we used a multicolor blackbody emission model accounting for thermal radiation from the accretion disk. For the case of maximally rotating black hole (spin a = 0.998), we were able to reconstruct both spin and inclination of the system with a high precision (∆a ≤ 0.2 for spin and ∆θ ≤ 15 deg for inclination). For less rotating black holes, the spin was correctly recovered, but with a large uncertainty. The inclination is well constrained for any spin value. We conclude that polarimetric measurements will be useful to make independent black hole spin measurements, that would be compared with the spectral-fitting and timing methods. Therefore, X-ray polarimetric missions will be highly desirable. 1

This Thesis, entitled Utilization of Flotation tailings in the Construction Business, has been formulated and developed in the Darkov and ČSM Coal Mines. All the findings acquired in the abovementioned mines will be used as basic information for the future utilization of this fine-grained waste, which is a by-product of black coal processing. While developing and writing this Thesis, I was allowed to observe the processing at both the Darkov and ČSM Coal Mines. The theoretical part of this Thesis is dedicated to the description of processing of black coal, from the moment of extraction to the point of expedition or storage appropriate storage areas. Flotation tailings are composed of fine-grained waste created during flotation processing of black coal. The flotation tailings are deposited (floated) into an assigned depository area - the Pilňok tailings pond. The theoretical part of the Thesis also deals with the consequences of coal extraction, which impact the natural environment, and with reparatory actions undertaken to alleviate such consequences. Finally, a chapter within the theoretical part is also dedicated to the possibilities of utilization of flotation tailings, followed by the legislative framework that governs the processing of flotation tailings and an associated certification process. The practical part of the Thesis lists the results of flotation tailings sample examination, which is essential for product certification. The Conclusion evaluates the examination results and the requirements of the Cihelna Polom s.r.o. (Polom Brick Factory, ltd.) with regard to the future long-term utilization of flotation tailings in the production of brick products.

This diploma thesis deals with proposal of geocaching oriented educational trails in Ostrava-Karvina region on which stops are placed already existing caches or suggestions of their placement. Given that coal mining has more than two hundred year long tradition in this area, every stop on trails with caches are mining oriented. Basic problematic concerning this topic is outlined in literature overview while the research part of this thesis is focused on draft of 4 different educational trails with mining theme consisting either thorough description of already existing caches or newly designed ones. Research part also contains a questionnaire given to active cachers which aim was to determine the interest in said trails and their overall potential. Lastly the research part was complemented by guided interview with experienced cacher. In conclusion of the thesis are formulated drafts for utilization of these educational trails.

Hard X-ray spectra of accreting black holes in active galactic nuclei and X- ray binaries are characterized by a power-law shape with an exponential cut-off energy at several tens up to few hundreds of keV. The value of the cut-off energy is related to the temperature of a hot corona that reprocesses and inversely Comptonizes thermal emission from the accretion disc. The exact geometry of the corona is still unknown. Several observations suggest it to be very compact and in a close proximity to the black hole. This implies strong relativistic effects such as gravitational redshift, Doppler shift, light bending and beaming to shape the resulting spectra. However, the relativistic effects on primary X-ray emission are often neglected in the data spectral fitting. In this work, we investigate how large uncertainty is introduced by neglecting these relativistic effects. To this purpose, we performed simulations of X-ray spectra for different coronal geometries, and compared the intrinsic and observed values of the cutoff energy. We re-analyzed NuSTAR observations of an active galactic nucleus 1H0419-577 and X-ray binary GRS 1915+105. We found that the extremely low coronal temperatures observed in these sources may be explained by the gravitational redshift due to the proximity of the compact corona to the black hole....

This masters’ thesis deals with a thermal design of a draft dry bottom boiler for bituminous coal that should replace a disassembled boiler in a current boiler room. Application of SCR is intended in order to reach emission standards of NOx.

As a non-linear theory of space-time, general relativity deals with interesting dynamical systems which can be expected more prone to chaos than their Newtonian counter-parts. In this thesis, we study the dynamics of time- like geodesics in the static and axisymmetric field of a Schwarzschild black hole surrounded, in a concentric way, by a massive thin disc or ring. We reveal the rise (and/or decline) of geodesic chaos in dependence on parameters of the sys- tem (the disc/ring mass and position and the test-particle energy and angular momentum), (i) on Poincaré sections, (ii) on time series of position and their power spectra, (iii) by applying two simple yet powerful recurrence methods, and (iv) by computing Lyapunov exponents and two other related quantifiers of or- bital divergence. We mainly focus on "sticky" orbits whose different parts show different degrees of chaoticity and which offer the best possibility to test and compare different methods. We also add a treatment of classical but dissipative system, namely the evolution of a class of mechanical oscillators described by non-standard constitutive relations.

The consequences of two key approximations of accretion-disc physics near black holes are studied in this thesis. First, the question of effective ``pseudo-Newtonian" potentials mimicking a black hole is investigated both through numerical simulations and analytical means, and second, the neglect of additional gravitating matter near accreted-upon black holes and its consequences are put to test. After some broader discussion of integrability, resonance and chaos, a general "pseudo-Newtonian" limit for geodesic motion is derived, and applied for the case of null geodesics near a glowing toroid and for time-like geodesics in the Kerr metric. Afterwards, a new Newtonian gravitational potential for non- singular toroids is proposed and its usefulness for the so-called Weyl space-times is discussed. Finally, a new pseudo-Newtonian potential is introduced and applied alongside already known potentials in models of free test particle motion in the field of a black hole with a disc or ring, in complete analogy with previous exact-relativistic studies, and the previous conclusion of chaos in disc/ring-hole models is confirmed. Overall, the pseudo-Newtonian framework is able to reproduce a number of key features of the original systems with notable differences arising only as a consequence of extremely strong or...

Stars can be stretched and ripped apart by the super-massive black hole at the core of a galaxy. The remnant gaseous trail gradually circularizes in a ring of mass that spreads by the viscous forces into an accretion disc. In this thesis we have studied the spectral line profle time evolution of radiation refected by the accretion disc located around a super-massive black hole. We assume the central body to be a slowly rotating or non-rotating super-massive black hole with no charge, in the frst approximation represented by the Schwarzschild solution. In a sense of Shakura-Sunyaev standard accretion disc model with the kinematic viscosity parameter α ≈ 1 we allow the accretion disc evolution to be guided by the angular momentum transfer equation with the initial mass ring located at the tidal radius being the product of tidal disruption of a star passing by a super-massive black hole. During the simulations we keep varying the mass of the central body while we keep the mass and the radius of the star constant (M = 1M⊙ and R = 1R⊙), i.e. taking into account the solar-type stars only. We defer the prospects of the full analysis involving spin (and charge) of the central body for the future study as it will be necessary to use the equations for the redshift factor and the accretion disc evolution...