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Gravitační vlny v expandujících vesmírech
Pavičevič, Mak ; Bičák, Jiří (advisor) ; Kofroň, David (referee)
in English In the present work we are analysing the asymptotic behaviour of vacuum spacetimes describing gravitational waves in universes with anisotropic expansion. The thesis is divided into two main parts. In the first chapter we review cylindrical gravitational waves and their cosmological generalizations; Bondi-Sachs formalism, Penrose's null infinity and the peeling property of the Riemann tensor are summarized. Symmetry reduction, a (2+1)-dimensional formalism, is presented in detail and used in calculations. Generalization of the symmetry reduction to other dimensions and relation to Brans-Dicke theory is carried out. In the second chapter we analyse solutions describing cosmological gravitational waves proposed in the literature and discuss their relation to boost-rotation symmetric spacetimes. After utilizing the symmetry reduction, Kasner and Bianchi VI models are chosen as background solutions. The behaviour of the metric is encoded in a single function, a solution to the linear wave equation. The full solution is then a superposition of the gravitational wave representing, for example, pulses, and the background one. We calculate the Riemann and the Cotton tensor components of the 3-spacetimes and discuss the conformal completion. A comparison with four-dimensional behaviour is also...
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Conservation laws with respect to curved backgrounds associated with black holes and cosmological models
Pavičevič, Mak ; Bičák, Jiří (advisor) ; Schmidt, Josef (referee)
in English We review the problem of defining energy, momentum etc. and their con- servation in curved spacetimes and a possible resolution in the form of a background spacetime. Our focus is set on superpotentials, which, when in- tegrated on a spatial boundary, yield conserved charges, while a conserved vector current is a divergence of a superpotential. Within this thesis, we build a minimal mathematical formalism necessary to prove and interpret Noether's theorem which unites symmetries and conservation laws. We em- phasize the significance of Killing vector fields - generators of isometries. After a short historical overview, the KBL superpotential is presented in de- tail, which makes it possible to define conserved quantities with respect to a curved background spacetime. We then employ its generalization within the Horndeski scalar-tensor theory of gravity. We concentrate on a subclass con- taining non-minimal derivative coupling of the Einstein tensor and a scalar field. We find superpotentials for spherically symmetric, static spacetimes (e.g. exterior of black holes) and time-dependent cosmological spacetimes, in particular with respect to (Anti-)de Sitter backgrounds. 1
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