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Study of spacetime of two static black holes
Zámyslický, Dominik ; Krtouš, Pavel (advisor) ; Švarc, Robert (referee)
The main goal of this thesis is to find a new set of coordinates to visualize the Weyl solution representing two black holes kept in equilibrium. New coordinates should pic- ture the horizons of the black holes, degenerated in Weyl's coordinates into two linear objects on the axis, as spherical-like objects. These coordinates are constructed based on comparing two potentials that solve the Poisson equation with two-point and two- linear-segment sources. It includes an introduction of a new coordinate complementary to the potential coordinate and the axisymmetric coordinate. We examine the properties of these coordinates and discuss their interesting points and lines. We also consider the multipole expansion of the discussed systems. 1
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Properties and interpretation of black hole spacetimes
Polášková, Eliška ; Krtouš, Pavel (advisor) ; Houri, Tsuyoshi (referee) ; Kubizňák, David (referee)
In this thesis, we study a limit of the Kerr-(A)dS spacetime in a general dimen- sion where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts: the first part has the form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire spacetime, but only for the directions not subjected to the limit, and the second part can be interpreted as the Kähler metrics. However, this separation is only valid for tangent spaces and it is not integrable, thus it does not lead to independent manifolds. We also reconstruct the origi- nal number of explicit and hidden symmetries associated with Killing vectors and Killing tensors. Therefore, the resulting spacetime represents a special case of the generalized Kerr-NUT-(A)dS metric studied before that also retains the full Killing tower of sym- metries. In D = 6, we present evidence of an enhanced symmetry structure after the limit. Namely, we find additional Killing vectors and show that one of the Killing tensors becomes reducible as it can be decomposed into Killing vectors. 1
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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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Black holes in string theory
Kudrna, Matěj ; Schnabl, Martin (advisor) ; Krtouš, Pavel (referee)
Recently it was shown by M. Guica, T. Hartman, W. Song and A. Strominger that the entropy of extreme Kerr black hole can be computed through a duality between the quantum gravity on the background of the Kerr black hole and the conformal field theory near the horizon. In our diploma work we have found a generalization of this procedure: we leave the near horizon geometry and we define our boundary conditions and the surface charges in the full spacetime on the horizon of the black hole, where the dual conformal field theory "lives". We use this procedure to rederive the entropy of extremal black holes and then we compute the entropy of general rotating black holes.
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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)
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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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