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Horizons of type D black holes
Ovcharenko, Hryhorii ; Podolský, Jiří (advisor) ; Maeda, Hideki (referee)
In this thesis, we investigate the properties of horizons appearing in the most general black-hole electrovacuum solution of algebraic type D. Firstly, we analyze the completely general type D solution, found by Debever, Kamran, and McLenaghan, and show that the only subsolution corresponding to black holes is the Plebanski-Demianski one. Then we demonstrate that all horizons within the Plebanski-Demianski family are regular, mean- ing that all curvature scalars and Riemann tensor components in the proper tetrad are finite. Moreover, we systematically explore the possible degeneracy of horizons within the Plebanski-Demianski class of spacetimes. Despite it being impossible for all four hori- zons to coincide, there are still several configurations of degenerate (extremal) horizons in which there is no thermal radiation from the corresponding black hole. Subsequently, we focus on constructing a set of coordinates that are adapted to freely-falling observers and are regular on the horizon, generalizing thus the Doran coordinates to the Plebanski- Demianski family of spacetimes. We demonstrate that this generalization is not unique, and different approaches are more suitable for different situations. 1
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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
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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.
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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
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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.
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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.
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