|
|
Investigation of geometrical and physical properties of exact spacetimes
Hruška, Ondřej ; Podolský, Jiří (advisor) ; Pravda, Vojtěch (referee) ; Steinbauer, Roland (referee)
In this work, we study geometrical and physical properties of exact spacetimes that belong to non-expanding Pleba'nski-Demia'nski class. It is a family of solutions of type D that also belong to the Kundt class, and contain seven arbitrary parameters including a cosmological constant. We present here the results of three extensive articles, each focusing on a different aspect of the problem. In the first article, we investigate the meaning of individual parame- ters in the non-expanding Pleba'nski-Demia'nski metric. First, we set almost all parameters to zero and obtain Minkowski and (anti-)de Sitter backgrounds. Af- terwards, we allow other parameters to be non-zero and we study the B-metrics, non-singular "anti-NUT" solutions and conclude with the full electrovacuum Pleba'nski-Demia'nski metric. In the second article, we focus on the de Sitter and anti-de Sitter backgrounds where we present and analyse 11 new diagonal metric forms of (anti-)de Sitter spacetime. We find five-dimensional parametriza- tions, draw coordinate surfaces and conformal diagrams. In the third article, we show that the AII-metric together with the BI-metric describes gravitational field around a tachyon on both Minkowski and (anti-)de Sitter backgrounds. Fi- nally, in order to better understand the global structure and...
|
|
|
Spacetimes with accelerating sources
Vrátný, Adam ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
The core of this thesis is the analysis of accelerating black hole solution with the NUT parameter, which was found by Chng, Mann and Stelea in 2006, and related spacetimes. The original work consists of three interconnected parts. In the first chapter we study the Taub-NUT solution, in particular the nature of its pathological axes, and we include a number of visualizations. In the second chapter we investigate the accelerating Taub-NUT solution, we present it in a new form, and we discuss its "deviation" from the Pleba'nski-Demia'nski class of solutions. To see the differences more clearly, in the final chapter we put also the Pleba'nski-Demia'nski metric into a completely new factorized form. The work is concluded by discussion of special subcases, from which it is clearly seen that the Pleba'nski-Demia'nski class does not contain the accelerating Taub-NUT solution.
|
|
|
The study of exact spacetimes with a cosmological constant
Hruška, Ondřej ; Podolský, Jiří (advisor)
In this work we investigate an exact solution of Einstein's equations which is described by the Pleba'nski-Demia'nski metric. This metric represents type D space-times and contains seven free parameters, including electric and magnetic charges and a cosmological constant. We study geometrical and phy- sical properties of these space-times in the case when repeated principal null congruences have zero expansion. Therefore, first we study de Sitter universe and anti-de Sitter universe in the Pleba'nski-Demia'nski coordinates, and we care- fully analyze the corresponding parametrizations of (anti-)de Sitter hyperboloid in five-dimensional flat space-time, unknown so far, we draw the respective con- formal diagrams, and we find transformations to various known forms. After that, we investigate the more general case of the B metrics with a cosmological con- stant, and we do a basic analysis of its geometrical properties. We summarize the article by Gott from 1974, where he interprets the BI metric as a part of space-time with a tachyon singularity, and we generalize his results for the case of non-zero cosmological constant. Finally, we analyze even more general cases of the Pleba'nski-Demia'nski metric with more non-zero parameters. In particular, we study the electromagnetic field in the case of non-zero...
|
|
| |
|
|
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
|
|
|
Study of accelerating Taub-NUT spacetimes
Vrátný, Adam ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
In this work we investigate recent publication by Brenda Chng, Robert Mann and Cristian Stelea in which a new accelerating Taub-NUT black hole metric was found. We verify that it is indeed a vacuum solution of Einstein's field equations, we find its principial null directions, and determine the algebraical type of the spacetime. We prove that this spacetime is algebraicaly general, so that it can not be contained in the Plebański-Demiański type D class. We also derive a new form of this metric which is convenient for obtaining its special cases, namely the standard forms of C-metric, Taub-NUT metric, and Schwarzschild metric. Powered by TCPDF (www.tcpdf.org)
|
|
|
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)
|
|
|
The study of exact spacetimes with a cosmological constant
Hruška, Ondřej ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
In this work we investigate an exact solution of Einstein's equations which is described by the Pleba'nski-Demia'nski metric. This metric represents type D space-times and contains seven free parameters, including electric and magnetic charges and a cosmological constant. We study geometrical and phy- sical properties of these space-times in the case when repeated principal null congruences have zero expansion. Therefore, first we study de Sitter universe and anti-de Sitter universe in the Pleba'nski-Demia'nski coordinates, and we care- fully analyze the corresponding parametrizations of (anti-)de Sitter hyperboloid in five-dimensional flat space-time, unknown so far, we draw the respective con- formal diagrams, and we find transformations to various known forms. After that, we investigate the more general case of the B metrics with a cosmological con- stant, and we do a basic analysis of its geometrical properties. We summarize the article by Gott from 1974, where he interprets the BI metric as a part of space-time with a tachyon singularity, and we generalize his results for the case of non-zero cosmological constant. Finally, we analyze even more general cases of the Pleba'nski-Demia'nski metric with more non-zero parameters. In particular, we study the electromagnetic field in the case of non-zero...
|
|
|
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.
|
|
|
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.
|
guest ::
RSS feed.