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Inhomogeneous cosmology and averaging methods
Kašpar, Petr ; Svítek, Otakar (advisor) ; Balek, Vladimír (referee) ; Carloni, Sante (referee)
In this work we have examined different methods of averaging in general relativity and cosmology. We developed the method based on Cartan scalars. We computed the backreaction term for a flat LTB model with a special ansatz for the radial function. We found out that it behaves as a positive cosmological constant. In the next part of this thesis we were interested in averaging inside LRS class II dust model. For this family we averaged all the Einstein equations and the resulting system generalizes the Buchert equations. We numerically worked out two concrete examples where deceleration parameter changes its sign from positive to negative. Powered by TCPDF (www.tcpdf.org)
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Inhomogeneous cosmological models
Vrba, David ; Svítek, Otakar (advisor) ; Pravda, Vojtěch (referee) ; Žofka, Martin (referee)
In this work we study inhomogeneous cosmological models. After a brief review of applications of inhomogeneous solutions to Einstein equations in cosmology, we give a short description of the most widely used inhomogeneous cosmological models. In the second chapter we study in detail geometrical prop- erties of the Szekeres spacetime and we are concerned with the interpretation of the metric functions in different types of geometries. In the last chapter we model inhomogeneity in Szekeres spacetime. We derive formula for the density contrast and investigate its behaviour. We also derive conditions for the density extremes that are necessary for avoiding the shell crossing singularity in Szekeres spacetime. 1
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Dynamics of causal sets
Káninský, Jakub ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
The causal set theory represents a possible approach to quantum gravity. It is based upon two leading concepts, causality and discreteness. The causal set, embodying the fundamental structure, forms the discrete substratum for spacetime. Relations to the continuous spacetime are then studied by kinematics while the dynamics' task is to provide a set of rules that would conduct the process of formation. Within this thesis we give a coherent introduction to the causal set theory, focusing on the classical dynamics, in particular its general form called the classical sequential growth. In the sequel, we explore some of the applications, taking advantage of growth simulations.
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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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Interaction of gravitational radiation with matter
Tintěra, Tomáš ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In the present work we study gravitational waves in the approximation of high frequency, and their interaction with matter waves with comparable frequency. We generalize the formalism of R. A. Isaacson to the case of non-vacuum spacetimes. We formulate and study a technique of so called averaging, which helps us to separate slow changes and high-frequency fluctuations of various tensor fields. The described methods are used in examples with a given particular metric - so called background metric. We thus study the interaction of high-frequency gravitational waves on the Robinson- Trautman background and the high-frequency electromagnetic waves. Further, we seek a perfect fluid with high-frequency energy-momentum tensor that could coexist with high-frequency gravitational waves on the flat Friedmann-Lemaˆıtre-Robertson-Walker background; again, we examine the relation between those potential gravitational and matter waves.
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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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Classical limit of relativistic dynamical fields
Hruška, Ondřej ; Podolský, Jiří (advisor) ; Svítek, Otakar (referee)
In this work, we summarise existing results concerning the absence of "gravitational aberration" in Einstein's general theory of relativity, i.e., the fact that the gravitational "force" points towards the instantaneous position of objects with mass, although the field propagates at the speed of light. The electromagne- tic interaction behaves similarly. Thanks to that, the classical limit with infinite speed of propagation of electricity and gravitation is a good approximation of relativistic fields. We use the Liénard-Wiechert potentials to compute the corre- sponding electric field, and the Christoffel symbols calculated from the metric of so-called photon rocket to determine the gravitational acceleration. We analyse the magnitude and direction of the interaction in both cases. Our own contri- bution is an attempt to interpret the direction of gravitation interaction in the context of de Sitter universe with non-zero cosmological constant.
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Properties of near-horizon geometry of spacetimes
Daněk, Jiří ; Žofka, Martin (advisor) ; Svítek, Otakar (referee)
Nowadays, the near-horizon regions of black holes have enjoyed great attention thanks to their role in the popular AdS/CFT correspondence and their specific geometry suitable for formulations of uniqueness theorems in higher dimensions. A strictly general-relativistic point of view reveals also many interesting phenomena taking place near black-hole horizons. Our aim was to investigate how horizon multiplicity affects near-horizon geometry, geodesical distance, radial motion of photons and massive, charged particles, and also the possibility of collision processes leading to unbound collision energies near the horizon. We chose the Reissner-Nordström-de Sitter metric, which, on the one hand, is simple thanks to being static and spherically symmetric but which, on the other hand, is rich enough to enable the existence of up to a doubly degenerate ultra-extreme horizon. After discussing the physical feasibility of the near-horizon limit, we applied it to single, double, and triple horizons, their near-horizon geometries, and local collision processes. We found continuous coordinate systems covering all types of horizons and analytic solutions for motion of radial photons and special or critical, massive, charged particles in their vicinity. We addressed particle collisions in the immediate vicinity of horizons...
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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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