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Chaos v porušených polích černých děr
Witzany, Vojtěch ; Semerák, Oldřich (advisor) ; Heyrovský, David (referee)
The loss of complete geodesic integrability is one of the important consequences (and thus indicators) of deviation from the Kerr-type space-time. Indeed, it has been confirmed many times in the literature that even a highly symmetric perturbation of the Kerr or Schwarzschild metric can make the free test-particle motion chaotic. In this thesis, we study the test-particle dynamics in the field of a Schwarzschild black hole surrounded by a thin disc or ring, using, however, Newton's gravity with a simple "pseudo- Newtonian" potential to mimic the black hole. The Poincaré sections show that the (pseudo-)Newtonian system is slightly more chaotic than the general relativistic one. The difference seems to be correlated with the phase-space allowed region being more open towards the center in the pseudo-Newtonian case. Powered by TCPDF (www.tcpdf.org)
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Částice a pole v křivých prostoročasech (vybrané problémy)
Hejda, Filip ; Bičák, Jiří (advisor) ; Krtouš, Pavel (referee)
In 2009 Bañados, Silk and West described the possibility of principally unbounded collision energies in the centre-of-mass frame for the particle collisions in the vicinity of black holes. Their work attracted a big response. This thesis aims to summarise the results of a number of the articles about the topic and puts these results into a new, broader context. It also presents some generalisations of the existing results, especially for models of magnetised black holes. The main subject of interest is the question, whether the unbounded collision energies can be achieved in a single-scattering or multiple-scattering process which was first formulated by Grib, Pavlov and Zaslavskii. Variety of methods is summarised. A considerable attention is paid to the limiting near-horizon description, which is further developed in order to derive new links and relations among known results, particularly between the purely theoretical work dealing with the geometry of degenerate horizons and their vicinity and more astrophysical articles about magnetic fluxes. Powered by TCPDF (www.tcpdf.org)
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Numerical evolution of black-hole spacetimes
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Palenzuela, Carlos (referee)
吀e so-called "trumpet" initial data has recently received mu挀 a琀ention as a potential candidate for the natural black hole initial data to be used in 3+1 numerical relativity simulations with 1+log foliation. In this work we first derive a variant of the maximal trumpet initial data that is made to move on the numerical grid by the means of a Lorentz boost and write a numerical code that constructs this boosted trumpet initial data. We also write a numerical code for calculating the Krets挀mann scalar from the 3+1 variables, to be used in analysing the data from our simulations. With the help of those two codes, we study the behaviour of the boosted trumpet initial data when evolved with the BSSN formulation of the Einstein equations, using 1+log slicing and the Γ-driver shi昀 condition.
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Properties of the extreme charged black hole near horizon
Hejda, Filip ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee)
It is known, that there exists a limiting correspondence between certain part (including the horizon) of extremal case of Reissner-Nordström space-time and Robinson-Bertotti space-time and that different generalisations of this near-horizon limit are possible. The aim of the presented work is to examine some of the properties of such limiting transitions. Firstly it is stressed how the global structure is reflected in the limit and secondly which properties of the space-time do provide that physical distances are preserved in the limit. Besides the extremal case the subextremal and hyperextremal generalisations are studied. As a complementary topic, the global extremal limit is stated. That means a transition from a generalised (non-symmetrical) conformal diagram of the subextremal case to the conformal diagram of the extremal case of Reissner-Nordström solution.
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Geometry inside deformed black holes
Basovník, Marek ; Semerák, Oldřich (advisor) ; Svítek, Otakar (referee)
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.
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New challenges in managing Liquidity risk - Liquidity Black Holes
Holovka, Martin ; Witzany, Jiří (advisor) ; Burešová, Jana (referee)
Following the financial turmoil in 2007/2008 liquidity black holes (LBH) has become arising topic often discussed among academics as well as portfolio managers all around the world. More recent view on liquidity risk covers those liquidity black holes which occur when the liquidity completely dries up in a particular market and the market becomes one-sided. There are basically 2 channels through which liquidity can be affected - Demand and Supply. In first case, the portfolios of investors lose the value and consequently the investors lose confidence in financial system. In the second case, banks hit their capital constraints, they tighten the terms of providing credits and loans to reduce the credit risk exposure and hence it becomes more difficult for firms to raise the funds. At this point dangerous spiral arises and the liquidity of financial system evaporates rapidly. The crucial point of this master thesis is to find the main determinants of Liquidity Black holes and find possible solutions to avoid their appearance.
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