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Algebraically special spacetimes - geometrical properties
Kuchynka, Martin ; Pravdová, Alena (advisor) ; Švarc, Robert (referee)
In the thesis, we set out to study a certain class of algebraically special spacetimes in arbitrary dimension. These are the so-called spacetimes of Weyl and traceless Ricci type N. Our work can be divided into two parts. In the first part, we study general geometrical properties of spacetimes under consideration. In particular, we are interested in various properties of aligned null directions - certain significant null directions associated with algebraic structure of the Weyl and the Ricci tensor. Since the obtained results are of geometric nature, they are theory-independent and thus hold in Einstein's gravity as well as in its various generalizations. In the second part of our work, we apply these general results in the Einstein-Maxwell p-form theory, within which spacetimes of traceless Ricci type N emerge naturally as a part of a solution of the Einstein-Maxwell equations with a null Maxwell field. Powered by TCPDF (www.tcpdf.org)
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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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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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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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Algebraic classification of the Weyl tensor
Pravdová, Alena
Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.
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