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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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Structure and dynamics of shell sources in general relativity
Turnovec, Aleš ; Žofka, Martin (advisor) ; Langer, Jiří (referee)
Cylindrically symmetric shell sources are studied and a general form of induced energy-momentum tensor of a collapsing shell is presented. The actual movement of the shell is numerically solved for a case when dynamics of the system is determined by energy conservation per unit length. It is then shown that additional assumptions can prevent the collapse, e. g. induced energy-momentum tensor as perfect fluid or null dust of counter-rotating particles. Collapse can be prevented also by introducing Thorne's C-energy into the system.
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Generating Methods in GR and Properties of the Resulting Solutions
Hruška, Jakub ; Žofka, Martin (advisor) ; Pravdová, Alena (referee) ; Gürlebeck, Norman (referee)
The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1
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Gravitation in higher dimensions
Kubíček, Jan ; Pravdová, Alena (advisor) ; Žofka, Martin (referee)
The thesis starts with a brief introduction to the algebraic classificati- on of tensors and spacetimes in higher dimensions. Attempts to generalize the Goldberg-Sachs theorem are also discussed. There is a summary of main results for optical matrices of algebraically special spacetimes in higher dimensions. The optical matrix for a type III spacetime in six dimensions is found using Bianchi identities. A few properties of type III optical matrices in a general dimension are also found. Various properties of equations obtained from Bianchi identities for type III spacetimes are studied in appendices. 1
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Charged particles in spacetimes with an electromagnetic field
Veselý, Jiří ; Žofka, Martin (advisor)
The subject of study of this thesis is the Kerr-Newman-(anti-)de Sitter space- time, a rotating and charged exact black-hole solution of the Einstein-Maxwell equations with a non-zero cosmological constant. In the first part of the thesis we examine admissible extremal configurations, present the corresponding Penrose diagrams, and investigate the effects of frame-dragging. In the second part, we follow the motion of charged particles via the Lagrangian formalism, focusing on the equatorial plane and the axis where we arrived at some analytic results con- cerning the trajectories. Static particles, effective potentials and - in the case of the equatorial plane - stationary circular orbits are examined. We also perform numerical simulations of particle motion to be able to check our analytic results and also to foster our intuition regarding the behaviour of the test particles. The last part concerns quantum tunnelling of particles through the space-time's hori- zons, specifically the null geodesic method. The main goal of these computations is to obtain horizon temperatures, in which we succeed up to a constant multi- plicative factor. We discuss various pitfalls of the method and stake out a possible approach when applying it to the extreme horizons present in KN(a)dS. 1
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