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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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