|
|
Kundt spacetimes in the Einstein-Gauss-Bonnet theory of gravity
Nicek, Filip ; Podolský, Jiří (advisor) ; Pravdová, Alena (referee)
In this work, we study a complete family of non-expanding Lorentzian geome- tries with non-vanishing gyratonic terms in the Einstein-Gauss-Bonnet (EGB) theory of gravity of arbitrary dimension. First, we introduce the large Kundt class, defined geometricaly by admitting a non-expanding, twist-free, shear-free null geodesic congruence, and summarise the main results from Einstein's the- ory of gravity in an arbitrary dimension. We then systematically derive the field equations of EGB theory, analyse their main properties, and identify four distinct subclasses. Finally, we discuss the special case of fully general EGB pp-waves and EGB VSI/CSI spacetimes. i
|
|
|
Spacetimes with black holes
Vrátný, Adam ; Podolský, Jiří (advisor) ; Kubizňák, David (referee) ; Senovilla, José M. (referee)
In this thesis, we study exact black hole spacetimes of algebraic type D, which are a part of much wider Pleba'nski-Demia'nski class of solutions. We reformulate the well- known form of this metric and obtain new improved representation of this black hole family with simplified, explicit and (at least partially) factorized metric functions. This new form of the spacetimes allows us to gain the standard expressions for the well-known solutions such as the Kerr-Newman-NUT-(anti-)de Sitter black hole, accelerating Kerr- Newman-(anti-)de Sitter black hole, (possibly charged) Taub-NUT-(anti-)de Sitter black hole, accelerating Kerr-NUT-(anti-)de Sitter black hole, and their special cases in asymp- totically flat universe, just by putting the appropriate parameters to zero. We also provide a thorough physical and geometrical analysis of this new form of spacetimes. Furthermore, we analyze a solution corresponding to the accelerating Taub-NUT black hole, which was originally found by Chng, Mann and Stelea in 2006. We perform an in-depth analysis of this solution, and study its relation to the Pleba'nski-Demia'nski class.
|
|
|
Exact spacetimes in 2+1 gravity
Papajčík, Matúš ; Podolský, Jiří (advisor) ; Maeda, Hideki (referee)
We present a study of exact solutions to the coupled system of Einstein-Maxwell equations for Robinson-Trautman and Kundt geometries with a cosmological constant in 2+1 gravity. We also consider an electromagnetic field without any charges or currents. The equations are fully integrated for the nonexpanding Kundt family of spacetimes which only admit an aligned electromagnetic field, and for the aligned Robinson-Trautman class. A special subclass of these solutions is then identified as the charged black hole spacetime in 3D gravity. The nonaligned Robinson-Trautman solution decouples into a separated system of differential equations for the metric and the electromagnetic field. We show that the Robinson-Trautman spacetime admits a nonaligned electromagnetic field by finding a simple particular solution to the equations. Furthermore, we develop a new method of algebraic classification of spacetimes in three dimensions based on the projections of the Cotton tensor onto a suitable null basis. We then show that this classification is equivalent to the Petrov classification of the Cotton-York tensor in 2+1 gravity. 1
|
|
|
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.
|
|
|
Spacetimes with photon rockets
Kolář, Ivan ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
In this work we study exact spacetimes that represent the gravitational field of a localized object accelerating due to an anisotropic emission of photons - pho- ton rocket. First, we describe general properties of the Kinnersley and the Bonnor rocket, which both belong to the family of Robinson-Trautman spacetimes. Sub- sequently, we summarize two main approaches to the study of asymptotically flat spacetimes: the Bondi-Sachs and the Penrose methods, combined and modified by Tafel and Pukas in recent papers. We compare the mass aspect of the Robinson- Trautman spacetime obtained by both methods, and generalize thus the relation found by von der Gönna and Kramer. Next, we calculate the energy-momentum vector, the Bondi rest mass, and the "news tensor for the arbitrarily moving Kin- nersley rocket. By using these results, we naturally define the velocity vector of the rocket with respect to the Minkowski "background spacetime. We conclude with the physical interpretation of the Kinnersley rocket in various reference fra- mes.
|
|
| |
|
| |
|
| |
|
| |
|
|
Conformally flat solutions of Einstein's equations
Prikryl, Ondřej ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
The aim of this work is to study relations between some families of exact solutions of Einstein's gravitational field equations, in particular the conformally flat spacetimes with plain radiation (or analogous solutions of the algebraic type N) and a cosmological constant. Specifically, we present explicit transformations between the metric forms which have been recently found by Edgar and Ramos and solutions of the type found by Ozsváth, Robinson and Rózga that ar known since 1980's. Powered by TCPDF (www.tcpdf.org)
|
guest ::
RSS feed.