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The mathematical theory of perturbations in cosmology
Novák, Jan ; Pravda, Vojtěch (advisor) ; Chopovsky, A. (referee) ; Scholtz, Martin (referee)
We deal with cosmological perturbation theory in my work. We investigate General Theory of Relativity in Higher Dimensions in the Chapter 1. I mention GHP-formalism and algebraical classification of spacetimes. I use spinors to show that spacetimes of dimension 4 are special. I discuss also Kundt spacetimes, which are interesting for perturbation theory of black holes. I work with perturbations of FLRW ST's in GHP formalism in Chapter 2, which we want to use in Cosmological Inflation. The final part of my thesis is connected with scalar perturbations in f(R)-cosmologies, that can be used for explaining accelerated expansion in the last 5 billion years. I investigate the Universe at the scales of 150 Mpc, where I could not use the hydrodynamical approach. Thus I work with the generalization of the Landau's mechanical approach. I need quasi-static approximation for getting the potentials Φ and Ψ, since the equations are too complicated for direct integration. I plan to use the result also for numerical simulation of motions of dwarf galaxies in these potentials. Powered by TCPDF (www.tcpdf.org)
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The mathematical theory of perturbations in cosmology
Novák, Jan ; Pravda, Vojtěch (advisor) ; Scholtz, Martin (referee) ; Chopovsky, A. (referee)
We have been studying Cosmological Perturbation Theory in this thesis. There was presented the Standard General Relativity in higher dimensions. Then we used the apparatus of so called GHP formalism and this is a generalization of the well-known NP-formalism. Scalar perturbations in f(R)-cosmology in the late Universe is the final topic, which was a logical step how to proceed further and to continue in work where was shown that four-dimensional spacetimes are special. We get the potentials φ and ψ for the case of a box 150 Mpc. We used the so called mechanical approach for the case of a cosmological background. Our approach of getting these potentials is in observable Universe new. It is interesting also in the context of simulations in these, so called nonlinear theories. 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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Higher-dimensional Einstein gravity
Štrupl, František ; Podolský, Jiří (advisor) ; Pravda, Vojtěch (referee)
In the present work, we study some aspects of Einstein's theory of gravitation in general spacetimes with an arbitrary number of dimensions. In the first chapter we summarize the foundations of used geometric formalism and we derive the equation of goedesic deviation representing the relation between relative acceleration and the Riemann tensor. Second chapter presents different types of algebraic classification of the Weyl tensor in four and higher dimensions. Third chapter is devoted to a detailed examination of the test particle motions and also to the interpretation of different terms in the general equation of geodesic deviation. The fourth section examines appropriate choice of the interpretation frame and the coordinates. The final fifth chapter contains an analysis of the motion of test particles in the Robinson-Trautman spacetime with an arbitrary higher number of dimensions.
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General Relativity in Higher Dimensions
Málek, Tomáš ; Pravda, Vojtěch (advisor) ; Raeymaekers, Joris (referee) ; Podolský, Jiří (referee)
vii Title: General relativity in higher dimensions Author: Tomáš Málek Institute: Institute of Theoretical Physics Supervisor: Mgr. Vojtěch Pravda, PhD., Institute of Mathematics of the Academy of Sciences of the Czech Republic Abstract: In the first part of this thesis, Kerr-Schild metrics and extended Kerr- Schild metrics are analyzed in the context of higher dimensional general relativ- ity. Employing the higher dimensional generalizations of the Newman-Penrose formalism and the algebraic classification of spacetimes based on the existence and multiplicity of Weyl aligned null directions, we establish various geometri- cal properties of the Kerr-Schild congruences, determine compatible Weyl types and in the expanding case discuss the presence of curvature singularities. We also present known exact solutions admitting these Kerr-Schild forms and con- struct some new ones using the Brinkmann warp product. In the second part, the influence of quantum corrections consisting of quadratic curvature invariants on the Einstein-Hilbert action is considered and exact vacuum solutions of these quadratic gravities are studied in arbitrary dimension. We investigate classes of Einstein spacetimes and spacetimes with a null radiation term in the Ricci tensor satisfying the vacuum field equations of quadratic gravity...
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Algebraically special spacetimes in higher dimensions
Ducháček, Petr ; Pravda, Vojtěch (advisor) ; Žofka, Martin (referee)
In this thesis I show known solutions of Einstein's equations and I am trying to find if some of these solutions solve equations of quadratic gravity. I also show summary of decomposition of basic tensors in four and higher dimensions. I look in detail at Einstein spaces, null radiation and Kundt spacetimes. I also show other equations for relativity in higher dimensions. I come to equations that Einstein spaces and null radiation must satisfy in order to solve quadratic gravity. I also lay down the conditions that Kundt spacetimes must satisfy in order to be of certain Ricci type and Weyl type which is necessary to find new solutions of quadratic gravity.
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Study of Exact Spacetimes
Švarc, Robert ; Podolský, Jiří (advisor) ; Pravda, Vojtěch (referee) ; Steinbauer, Roland (referee)
In this work we study various aspects of the behaviour of free test particles in Einstein's general relativity and analyze specific physical properties of the background spacetimes. In the first part we investigate geodesic motions in the four-dimensional constant curvature spacetimes, i.e., Minkowski and (anti-)de Sitter universe, with an expanding impulsive gravitational wave. We derive the simple refraction formulae for particles crossing the impulse and describe the effect of nonvanishig cosmological constant. In the second part of this work we present a general method useful for geometrical and physical interpretation of arbitrary spacetimes in any dimension. It is based on the systematic analysis of the relative motion of free test particles. The equation of geodesic deviation is rewritten with respect to the natural orthonormal frame. We discuss the contributions given by a specific algebraic structure of the curvature tensor and the matter content of the universe. This formalism is subsequently used for investigation of the large class of nontwisting spacetimes. In particular, we analyse the motions in the nonexpanding Kundt and expanding Robinson--Trautman family of solutions.
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