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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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Spacetimes with photon rockets
Kolář, Ivan ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
In this work we study exact spacetimes that represent the gravitational field of a localized object accelerating due to an anisotropic emission of photons - pho- ton rocket. First, we describe general properties of the Kinnersley and the Bonnor rocket, which both belong to the family of Robinson-Trautman spacetimes. Sub- sequently, we summarize two main approaches to the study of asymptotically flat spacetimes: the Bondi-Sachs and the Penrose methods, combined and modified by Tafel and Pukas in recent papers. We compare the mass aspect of the Robinson- Trautman spacetime obtained by both methods, and generalize thus the relation found by von der Gönna and Kramer. Next, we calculate the energy-momentum vector, the Bondi rest mass, and the "news tensor for the arbitrarily moving Kin- nersley rocket. By using these results, we naturally define the velocity vector of the rocket with respect to the Minkowski "background spacetime. We conclude with the physical interpretation of the Kinnersley rocket in various reference fra- mes.
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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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Conformally flat solutions of Einstein's equations
Prikryl, Ondřej ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
The aim of this work is to study relations between some families of exact solutions of Einstein's gravitational field equations, in particular the conformally flat spacetimes with plain radiation (or analogous solutions of the algebraic type N) and a cosmological constant. Specifically, we present explicit transformations between the metric forms which have been recently found by Edgar and Ramos and solutions of the type found by Ozsváth, Robinson and Rózga that ar known since 1980's. Powered by TCPDF (www.tcpdf.org)
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