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Black hole thermodynamics
Milička, Marek ; Kubizňák, David (advisor) ; Tahamtan, Tayebeh (referee)
We use the basic techniques of general relativity to introduce black hole thermody- namics and directly address its relationship with classical thermodynamics. We give as many results explicitly calculated or directly cited as possible to make this thesis useful as a reference work. These results include calculation of surface gravity for a general spherical black hole and evaluation of Euclidean action for simple spacetimes, with the latter enabling one to fix the Bekenstein-Hawking formula for black hole entropy. We then consider the black hole phase transitions and give novel results showing that under simplifying assumptions Schwarzschild-AdS black hole is the only possible static black hole obeying the abridged virial expansion equation of state in the extended phase space.
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Multi-black-hole gravitational field
Klimešová, Eliška ; Žofka, Martin (advisor) ; Kubizňák, David (referee)
We study dynamics of an extremally charged black hole on the background of two stationary, mutually orbiting extremally charged black holes, forming thus a seed binary system. We extend the two-body perturbative solution of vacuum Einstein-Maxwell equations, known from literature, to the three body system. Restricting to slow-motion approximation and motion at a large distance, we de- rive the corresponding three-body Lagrangian and investigate limits of evolution of little- and large-mass black hole. Motivated by physical intuition and in order to check our results, we compare the former with solution of geodesic equation of an extremally charged test-body on identical background. Our results mainly consist of interpretation and comparison of characteristic motions. 1
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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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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 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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