
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 socalled universality. Classical fields exhibiting this property serve as exact solutions to virtually any higherorder 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 higherorder gravity theories. We illustrate this feature of almost universal metrics by finding new vacuum solutions to quadratic gravity and sixdimensional 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 higherorder modification of the EinsteinMaxwell theory. In particular, we identify solutions with this remarkable property as planefronted 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 EinsteinMaxwell 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 higherdimensional rotating blackhole spacetimes described by the KerrNUT(A)dS metric. In the first part, we examine spacetimes admitting a separable KleinGordon 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 KerrNUT(A)dS and specific EinsteinK¨ahler metrics. Then we consider a metric ansatz in the form of warped geometries of two KleinGordon separable metrics and classify the corresponding solutions. In the second part, we in vestigate a class of limits of the KerrNUT(A)dS spacetimes where particular roots of metric functions degenerate. Our limiting procedure results in various NUTlike and nearhorizon geometries such as the higherdimensional 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 KerrNUT(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 nonexistence of type II universal spacetimes in five dimensions.

 

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 socalled 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 theoryindependent 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 EinsteinMaxwell pform theory, within which spacetimes of traceless Ricci type N emerge naturally as a part of a solution of the EinsteinMaxwell equations with a null Maxwell field. Powered by TCPDF (www.tcpdf.org)


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 GoldbergSachs 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 ppwaves. 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 EinsteinMaxwell fields and it turns out that the admissible spacetimes are ppwaves again. However, if the method is generalized, it is possible to enlarge the class of conformal null EinsteinMaxwell 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 nontrivial 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.

 