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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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Geometry of 2+1 dimensional black holes
Klozová, Eliška ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee)
A boost Killing vector field with its isometry is considered in the 2+1 di- mensional anti-de Sitter spacetime. Then we choose two isometric surfaces and identify points that are on the same Killing orbit. An object locally isometric to the anti-de Sitter spacetime but with different global topology is obtained - the BTZ black hole. To prove that this object is really a black hole, a new adjusted coordinate system is introduced and the object's spacetime structure is explored. It is shown that such spacetime has outer and inner regions separated by the ho- rizon (null surfaces). We also show that parameter of the identification is closely related to the black hole's mass. Finally, we discuss limit transitions to other in- teresting physical objects with which we support setting of the zero energy-mass level. For understanding the geometry better, many three-dimensional pictures of the considered surfaces are included along with conformal diagrams of the BTZ black hole and also its space structure is depicted. 1
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Symmetries of anti-de Sitter universe and spaces obtained by identification along these symmetries
Irinkov, Pavel ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee)
Topological black holes in 2 + 1-dimensional AdS spacetime have seen a grad- ual increase in popularity over the last 20 years by their virtue of being one of the appropriate models to tackle the conceptual issues of quantum gravity in relatively simple setting. This work develops the classification of isometries of 2 + 1-dimensional anti-de Sitter spacetime and subsequently gives account of the solutions of the Einstein equations obtained by identifications along particular adapted coordinates. Special attention is paid to the Poincaré coordinates and extremal black holes and to a specific description of phase transition between conical singularities and black holes. 1
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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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Aplikace temporálních logik ve fyzice
Švarný, Petr ; Majer, Ondrej (advisor) ; Pudlák, Pavel (referee)
This thesis presents an introduction to the three main fields that study time: physics, philosophy, and logics. A brief introduction to general relativity, thermodynamics and quantum physics is made. Also some of the basic ideas from the philosophy of time are explained and dualities connected to time are described, e.g. eternalism vs. presentism, determinism vs. indeterminism and the reality or unreality of time. As there is a huge number of temporal logics, only the main ideas that differentiate these logics from others are pointed out and some typical proofs are then shown. Special attention is then given to the relation between logics and physics, how the first can be used in the latter. Thereafter, Branching space-times and Branching continuation models are presented, which proved to be useful within quantum physics. Next, some basic terminology connected to general relativity and the A, P and T topologies are introduced . These are used together with the given models to investigate a possible combination.
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Rovnice geodetiky v prostoročasech s helikální symetrií
Tomášik, Miroslav ; Scholtz, Martin (advisor) ; Žofka, Martin (referee)
In this bachelor thesis we investigate geodesics in helically symmetric spacetimes in the framework of linearized Einstein's gravity. Work is an extension of paper by Bičák, Scholtz and Bohata [2], which is under preparation. First we introduce standard numerical methods for solving systems of ordinary differential equations. Next we present helically symmetric solution of linearized Einstein's equations and numerical code solving the geodesic equation on given background. We discuss conditions of existence of helically symmetric solution and finally we present selected results obtained by numerical simulations. We give present few particular examples of geodesics, selected phase portraits obtained by the method of the Lyapunovov exponents and visualize the causal structure of helically symmetric spacetime.
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Thin discs and rings as sources of Weyl space-times
Kubíček, Jan ; Semerák, Oldřich (advisor) ; Žofka, Martin (referee)
Static and axially symmetric vacuum solutions of Einstein's equations can be descri- bed by the Weyl metric which only depends on two unknown functions, given by the Laplace equation and a line integral. In this thesis we study some properties of two Weyl space-times whose sources are one-dimensional rings - the Appell ring and the Bach-Weyl ring. On the behaviour of proper distances and geodesics in the central region we demonstrate that in Weyl coordinates these sources represent directional singularities. 1
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