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Gravitational Lensing by Substructures in Dark Matter Halos
Karamazov, Michal ; Heyrovský, David (advisor) ; Bartelmann, Matthias (referee) ; Dovčiak, Michal (referee)
Gravitational lensing serves as an invaluable tool for studying the distribution of mat- ter in the universe. This matter is predominantly dark and clumped into centrally concen- trated hierarchically structured halos of galaxies and galaxy clusters. Early comparisons suggested discrepancies between the high population of substructures predicted by cos- mological simulations and the lack of corresponding observational data. More recently, a major discrepancy in the opposite sense was reported from analyses of lensing galaxy clusters: the lensing efficiency of their substructures was found to be much higher than predictions based on cosmological simulations. In this thesis, we examine gravitational lensing by substructures embedded in dark-matter halos with Navarro-Frenk-White (NFW) density profiles. We start by a detailed investigation of a simple model with a single point mass perturbing the halo. Using analytical methods, we study its critical curves, caustics and their transitions. Next, we explore the geometry of lensed images and the weak-lensing characteristics of the same simple model, developing novel ways of their visualization. Finally, we construct a more realistic lens model of a galaxy cluster con- sisting of an ellipsoidal cluster halo combined with a population of truncated ellipsoidal galaxy...
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Exact spacetimes in modified theories of gravity
Karamazov, Michal ; Švarc, Robert (advisor)
In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1
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Exact spacetimes in modified theories of gravity
Karamazov, Michal ; Švarc, Robert (advisor) ; Podolský, Jiří (referee)
In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1
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Impulsive gravitational waves
Karamazov, Michal ; Švarc, Robert (advisor) ; Podolský, Jiří (referee)
In the review part of this bachelor thesis, we summarize various results about solutions to Einstein's gravitational field equations which describe both non-expanding and expanding impulsive gravitation waves in spacetimes of constant curvature. Special attention will be paid to geodesic motion in these spacetimes and to geometrical methods of their construction. In the original part of the thesis, we check compatibility of a direct solution to geodesic equation in (anti-)de Sitter spacetime with non-expanding impulsive wave and refraction formulae derived under the assumption of continuity of geodesics in a specific coordinate system. We also investigate an interaction of test particles with expanding spherical impulsive wave propagating on the Minkowski background which is generated by a pair of perpendicular snapping cosmic strings. Powered by TCPDF (www.tcpdf.org)
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