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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...
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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...
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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...
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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...
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