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Weyl metrics and their generalizations: classical and quantum viewpoint
Polcar, Lukáš ; Svítek, Otakar (advisor) ; Ledvinka, Tomáš (referee) ; Pound, Adam (referee)
In this thesis, we study two distinct topics both connected to stationary axially sym- metric spacetimes. The first is a study of an exact solution sourced by phantom scalar field. This solution can be derived from the well-known Curzon-Chazy metric and has several unusual features. It is a spherically symmetric wormhole which is however not symmetric with respect to its throat, it possesses a non-scalar curvature singularity and functions as a one-directional time machine. The energy content of the spacetime is ex- amined and various other properties are discussed. The remaining parts are dedicated to extreme mass ratio inspirals in two stationary axially symmetric spacetimes, perturbed Schwarzschild and Kerr. The canonical perturbation theory was used to transform the respective geodesic Hamiltonian to action-angle coordinates allowing us to evolve flux- driven inspirals in both spacetimes. 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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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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Macroscopic gravity
Kašpar, Petr ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
Due to the nonlinearity of the Einstein equations it is possible to obtain modified equations of the general relativity (with application in cosmology) just by averaging. One of the first covariant approaches to this problem is the theory of Macroscopic Gravity. Next proposed possibility is to first characterize spacetime by the Cartan scalars and then to proceed averaging procedure.
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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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Gravitational field of gyratons on various background spacetimes
Kadlecová, Hedvika ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee) ; Pravdová, Alena (referee)
In this work we have found and analyzed several gyraton solutions on various non-trivial backgrounds in the large Kundt class of spacetimes. Namely, the gyraton solutions on direct product spacetimes, gyraton solutions on Melvin universe and its generalization which includes the cosmological constant. These solutions are of algebraic type II. Also we have investigated type III solutions within the Kundt class and we have found the gyratons on de Sitter spacetime. We have generalized the gyraton solutions on direct product spacetimes to higher dimensions.
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