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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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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....
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Symmetries of systems in spaces related to high-dimensional black hole spacetime
Kolář, Ivan ; Krtouš, Pavel (advisor) ; Kubizňák, David (referee)
In this work we study properties of the higher-dimensional generally rotating black hole space-time so-called Kerr-NUT-(A)dS and the related spaces with the same explicit and hidden symetries as the Kerr-NUT-(A)dS spacetime. First, we search commuta- tivity conditions for classical (charged) observables and their operator analogues, then we investigate a fulfilment of these conditions in the metioned spaces. We calculate the curvature of these spaces and solve the charged Hamilton-Jacobi and Klein-Gordon equations by the separation of the variables for an electromagnetic field, which pre- serves integrability of motion of a charged particle and mutual commutativity of the corresponding operators.
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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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Quality improvements for citizen advice bureaux
Horčičková, Radka ; Vodáčková, Daniela (advisor) ; Kolář, Ivan (referee)
Hlavní podnětem k sepsání této bakalářské práce je jedinečné setkání dvou důležitých momentů. Prvním z nich je schválení konečné podoby zákona o sociálních službách a druhým je úspěšné ukončení projektu "Kvalita v občanských poradnách" realizovaného Asociací občanských poraden. Hlavním námětem této práce je kvalita služby občanského poradenství. Již několik let se kvalitou sociálních služeb zabývá Ministerstvo práce a sociálních věcí jako hlavní garant kvality sociálních služeb poskytovaných na území ČR. V následujících kapitolách bych ráda věnovala pozornost zavádění standardů kvality do občanského poradenství (§ 37 zákona o sociálních službách). Asociace občanských poraden jako garant kvality poskytovaných služeb členskými občanskými poradnami se již v několikaletém předstihu připravuje na avizované inspekce kvality iniciované Ministerstvem a v rámci své dobré praxe zavádí do systému řízení tzv. Standardy kvality občanských poraden. Zmiňovaný zákon (106/2006 Sb.) je z hlediska této práce významný, protože definoval oblasti ve kterých budou sociální služby poskytovány a dále stanovil pravidla pro tzv. povinnou registraci poskytovatelů sociálních služeb. Pravděpodobně již v příštím roce začne Ministerstvo práce a sociálních věcí rozbíhat tzv. inspekce kvality ve všech registrovaných zařízeních poskytujících...
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