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Geometry inside deformed black holes
Basovník, Marek ; Semerák, Oldřich (advisor) ; Svítek, Otakar (referee)
In this thesis we study exact general relativistic space-times generated by a black hole and an additional source of gravity, while restricting to two classes of static and axially symmetric solutions: the Majumdar-Papapetrou solution for a couple (in general, a multiple system) of extremally charged black holes and the "superposition" of a Schwarzschild black hole with the Bach-Weyl thin ring. We follow the effect of the additional source on the geometry of black-hole space-time on the behaviour of important invariants, in particular of the simplest scalars obtained from the Riemann and possibly also Ricci tensor. We have plotted the invariants both outside and inside the black hole; in the case of a Schwarzschild black hole with ring, we found, to this end, an extension of the metric below the horizon. It turns out that the external source may affect the geometry inside the black hole considerably, even in the vicinity of singularity, although the singularity itself remains point-like in both solutions studied here.
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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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Macroscopic gravity
Kašpar, Petr ; Žofka, Martin (referee) ; Svítek, Otakar (advisor)
Due to the nonlinearity of the Einstein equations it is possible to obtain modified equations of the general relativity (with application in cosmology) just by averaging. One of the first covariant approaches to this problem is the theory of Macroscopic Gravity. Next proposed possibility is to first characterize spacetime by the Cartan scalars and then to proceed averaging procedure.
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