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Matter Models in General Relativity with a Decreasing Number of Symmetries
Gürlebeck, Norman ; Bičák, Jiří (advisor) ; Fraundiener, Jörg (referee) ; Ledvinka, Tomáš (referee)
Title: Matter Models in General Relativity with a Decreasing Number of Sym- metries Author: Norman Gürlebeck Institute: Institute of theoretical physics Supervisor: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Abstract: We investigate matter models with different symmetries in general relativity. Among these are thin (massive and massless) shells endowed with charge or dipole densities, dust distributions and rotating perfect fluid solutions. The electromagnetic sources we study are gravitating spherical symmetric condensers (including the implications of the energy conditions) and arbitrary gravitating shells endowed with a general test dipole distribution. For the latter the Israel formalism is extended to cover also general discontinuous tangential components of the electromagnetic test field, i.e., surface dipole densities. The formalism is applied to two examples and used to prove some general properties of dipole distributions. This is followed by a discussion of axially symmetric, stationary rigidly rotating dust with non-vanishing proper volume. The metric in the interior of such a configuration can be determined completely in terms of the mass density along the axis of rotation. The last matter models we consider are non-axially symmetric, stationary and rotating perfect fluid solutions. This is done with a...
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Helical symmetry and the non-existence of asymptotically flat periodic solutions in general relativity
Scholtz, Martin ; Bičák, Jiří (advisor) ; Krtouš, Pavel (referee) ; Fraundiener, Jörg (referee)
1 Title Helical symmetry and the non-existence of asymptotically flat periodic solutions in general relativity Author Martin Scholtz Department Institute of theoretical physics Faculty of Mathematics and Physics Charles University in Prague Supervisor Prof. RNDr. Jiří Bičák, DrSc., dr. h.c. Abstract. No exact helically symmetric solution in general relativity is known today. There are reasons, however, to expect that such solutions, if they exist, cannot be asymptotically flat. In the thesis presented we investigate a more general question whether there exist periodic asymptotically flat solutions of Einstein's equations. We follow the work of Gibbons and Stewart [3] who have shown that there are no periodic vacuum asymptotically flat solutions an- alytic near null infinity I. We discuss necessary corrections of Gibbons and Stewart proof and generalize their results for the system of Einstein-Maxwell, Einstein-Klein-Gordon and Einstein-conformal-scalar field equations. Thus, we show that there are no asymptotically flat periodic space-times analytic near I if as the source of gravity we take electromagnetic, Klein-Gordon or conformally invariant scalar field. The auxilliary results consist of corresponding confor- mal field equations, the Bondi mass and the Bondi massloss formula for scalar fields. We also...
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Matter Models in General Relativity with a Decreasing Number of Symmetries
Gürlebeck, Norman ; Bičák, Jiří (advisor) ; Fraundiener, Jörg (referee) ; Ledvinka, Tomáš (referee)
Title: Matter Models in General Relativity with a Decreasing Number of Sym- metries Author: Norman Gürlebeck Institute: Institute of theoretical physics Supervisor: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Abstract: We investigate matter models with different symmetries in general relativity. Among these are thin (massive and massless) shells endowed with charge or dipole densities, dust distributions and rotating perfect fluid solutions. The electromagnetic sources we study are gravitating spherical symmetric condensers (including the implications of the energy conditions) and arbitrary gravitating shells endowed with a general test dipole distribution. For the latter the Israel formalism is extended to cover also general discontinuous tangential components of the electromagnetic test field, i.e., surface dipole densities. The formalism is applied to two examples and used to prove some general properties of dipole distributions. This is followed by a discussion of axially symmetric, stationary rigidly rotating dust with non-vanishing proper volume. The metric in the interior of such a configuration can be determined completely in terms of the mass density along the axis of rotation. The last matter models we consider are non-axially symmetric, stationary and rotating perfect fluid solutions. This is done with a...
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Helical symmetry and the non-existence of asymptotically flat periodic solutions in general relativity
Scholtz, Martin ; Bičák, Jiří (advisor) ; Krtouš, Pavel (referee) ; Fraundiener, Jörg (referee)
1 Title Helical symmetry and the non-existence of asymptotically flat periodic solutions in general relativity Author Martin Scholtz Department Institute of theoretical physics Faculty of Mathematics and Physics Charles University in Prague Supervisor Prof. RNDr. Jiří Bičák, DrSc., dr. h.c. Abstract. No exact helically symmetric solution in general relativity is known today. There are reasons, however, to expect that such solutions, if they exist, cannot be asymptotically flat. In the thesis presented we investigate a more general question whether there exist periodic asymptotically flat solutions of Einstein's equations. We follow the work of Gibbons and Stewart [3] who have shown that there are no periodic vacuum asymptotically flat solutions an- alytic near null infinity I. We discuss necessary corrections of Gibbons and Stewart proof and generalize their results for the system of Einstein-Maxwell, Einstein-Klein-Gordon and Einstein-conformal-scalar field equations. Thus, we show that there are no asymptotically flat periodic space-times analytic near I if as the source of gravity we take electromagnetic, Klein-Gordon or conformally invariant scalar field. The auxilliary results consist of corresponding confor- mal field equations, the Bondi mass and the Bondi massloss formula for scalar fields. We also...
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