National Repository of Grey Literature 11 records found  1 - 10next  jump to record: Search took 0.00 seconds. 
Universal solutions in gravity, electrodynamics and nonabelian gauge theories
Kuchynka, Martin ; Pravdová, Alena (advisor) ; Hervik, Sigbjorn (referee) ; Švarc, Robert (referee)
The presented thesis spans over a number of related topics with a com- mon theme - the so-called universality. Classical fields exhibiting this property serve as exact solutions to virtually any higher-order theory irrespective of the particular form of the field equations, being thus of particular interest in ef- fective field theories. The aim of this work is to study various aspects of such solutions in the context of gravity, electrodynamics, as well as more general nonabelian gauge theories. The results are concentrated in four chapters, the first of which is devoted to what we call the almost universal spacetimes. Due to their nice curvature properties, these spacetimes provide an efficient method for simplifying and solving the field equations of higher-order gravity theories. We illustrate this feature of almost universal metrics by finding new vacuum solutions to quadratic gravity and six-dimensional conformal gravity. In the second chapter, we shift our attention towards electrodynamics. Following up on recent results on universal electromagnetic fields, we deal with Einstein- Maxwell fields which simultaneously solve also any higher-order modification of the Einstein-Maxwell theory. In particular, we identify solutions with this remarkable property as plane-fronted gravitational and...
Selected exact spacetimes in Einstein's gravity
Ryzner, Jiří ; Žofka, Martin (advisor) ; McNutt, David D. (referee) ; Pravdová, Alena (referee)
The aim of this thesis is to construct exact, axially symmetric solutions of Einstein- Maxwell(-dilaton) equations, which possess a discrete translational symmetry along an axis. We present two possible approaches to their construction. The first one is to solve Einstein-Maxwell equations, the second one relies on a dimensional reduction from a higher dimension. We examine the geometry of the solutions, their horizons and singu- larities, motions of charged test particles and compare them. 1
Spacetimes with symmetries in a general dimension
Kolář, Ivan ; Krtouš, Pavel (advisor) ; Kubizňák, David (referee) ; Pravdová, Alena (referee)
In this work we study properties of spacetimes with a high degree of symme- try. Particularly, we focus on geometries related to higher-dimensional rotating black-hole spacetimes described by the Kerr-NUT-(A)dS metric. In the first part, we examine spacetimes admitting a separable Klein-Gordon equation. Motivated by Carter's work in four dimensions, we introduce a separable met- ric ansatz in higher dimensions. Analyzing Einstein's equations, we obtain the Kerr-NUT-(A)dS and specific Einstein-K¨ahler metrics. Then we consider a metric ansatz in the form of warped geometries of two Klein-Gordon separable metrics and classify the corresponding solutions. In the second part, we in- vestigate a class of limits of the Kerr-NUT-(A)dS spacetimes where particular roots of metric functions degenerate. Our limiting procedure results in various NUT-like and near-horizon geometries such as the higher-dimensional Taub- NUT-(A)dS spacetime. We demonstrate that the symmetries of the resulting geometries are enhanced, which is manifested by decomposition of Killing ten- sors into Killing vectors. The third part of this work deals with generalized symmetry axes of the Kerr-NUT-(A)dS spacetimes that are formed by fixed points of isometries. We show that some parts of the symmetry axes are sin- gular for nonzero NUT charges....
On type II universal spacetimes
Hervik, S. ; Málek, Tomáš ; Pravda, Vojtěch ; Pravdová, Alena
We briefly summarize our recent results on type II universal metrics of the Lorentzian signature. These metrics simultaneously solve all vacuum field equations of theories of gravity with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order. It turns out that the results critically depend on the dimensionality of the spacetime. While we discuss examples of type II universal metrics for all composite number dimensions, we have no examples for prime number dimensions. Furthermore, we have proven the non-existence of type II universal spacetimes in five dimensions.
On type N and III universal spacetimes
Hervik, S. ; Pravda, Vojtěch ; Pravdová, Alena
We briefly summarize our recent results on type N and III universal spacetimes.
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 (
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
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
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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2 Pravdová, Adéla
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