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Study of Exact Spacetimes
Švarc, Robert ; Podolský, Jiří (advisor) ; Pravda, Vojtěch (referee) ; Steinbauer, Roland (referee)
In this work we study various aspects of the behaviour of free test particles in Einstein's general relativity and analyze specific physical properties of the background spacetimes. In the first part we investigate geodesic motions in the four-dimensional constant curvature spacetimes, i.e., Minkowski and (anti-)de Sitter universe, with an expanding impulsive gravitational wave. We derive the simple refraction formulae for particles crossing the impulse and describe the effect of nonvanishig cosmological constant. In the second part of this work we present a general method useful for geometrical and physical interpretation of arbitrary spacetimes in any dimension. It is based on the systematic analysis of the relative motion of free test particles. The equation of geodesic deviation is rewritten with respect to the natural orthonormal frame. We discuss the contributions given by a specific algebraic structure of the curvature tensor and the matter content of the universe. This formalism is subsequently used for investigation of the large class of nontwisting spacetimes. In particular, we analyse the motions in the nonexpanding Kundt and expanding Robinson--Trautman family of solutions.
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Dynamical perturbations of triple stellar and planetary systems seen in gravitational waves with LISA
Mezera, Matěj ; Pejcha, Ondřej (advisor) ; Švarc, Robert (referee)
We study gravitational waves from a binary system that is perturbed by the presence of a distant third body. We present three representative models of the hierarchical triple system and we numerically model the gravitational waveform. The motion of the bodies is simulated in the Newtonian approximation on a long timescale so that Lidov-Kozai oscillation can occur. This oscillation causes periodic exchange between relative incli- nation and eccentricity of the inner binary. We analyze the frequency spectrum of the waveform and identify the effect of perturbations on a timescale similar to the binary orbital period Tin, perturbations related to the orbital period of the third body Tout, and Lidov-Kozai cycles with an approximate period T2 out/Tin. It is expected that the upcoming space detector LISA (Laser Interferometer Space Antenna) will be able to detect these gravitational signals and it will be possible to derive information about the triple system from the waveform. 1
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Study of Exact Spacetimes
Švarc, Robert
In this work we study various aspects of the behaviour of free test particles in Einstein's general relativity and analyze specific physical properties of the background spacetimes. In the first part we investigate geodesic motions in the four-dimensional constant curvature spacetimes, i.e., Minkowski and (anti-)de Sitter universe, with an expanding impulsive gravitational wave. We derive the simple refraction formulae for particles crossing the impulse and describe the effect of nonvanishig cosmological constant. In the second part of this work we present a general method useful for geometrical and physical interpretation of arbitrary spacetimes in any dimension. It is based on the systematic analysis of the relative motion of free test particles. The equation of geodesic deviation is rewritten with respect to the natural orthonormal frame. We discuss the contributions given by a specific algebraic structure of the curvature tensor and the matter content of the universe. This formalism is subsequently used for investigation of the large class of nontwisting spacetimes. In particular, we analyse the motions in the nonexpanding Kundt and expanding Robinson--Trautman family of solutions.
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Gravitational field of gyratons on various background spacetimes
Kadlecová, Hedvika
Title: Gravitational field of gyratons on various background spacetimes Author: Hedvika Kadlecová Department: Institute of Theoretical Physics Supervisor: doc. Pavel Krtouš, Ph.D. Supervisor's e-mail address: Pavel.Krtous@mff.cuni.cz Abstract: 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. Keywords: Kundt class of spacetimes, gravitational waves, Einstein-Maxwell equations, NP formalism Název práce: Gravitační pole gyratonů na pozadích různých prostoročasů Autor: Hedvika Kadlecová Ústav: Institut teoretické fyziky Školitel: doc. Pavel Krtouš, Ph.D. Školitelova e-mailová adresa: Pavel.Krtous@mff.cuni.cz Abstrakt: V této práci jsme nalezli a analyzovali několik různých gyratonových řešení na různých netriviálních pozadích z široké třídě Kundtových prostoročasů:...
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Dynamical perturbations of triple stellar and planetary systems seen in gravitational waves with LISA
Mezera, Matěj ; Pejcha, Ondřej (advisor) ; Švarc, Robert (referee)
We study gravitational waves from a binary system that is perturbed by the presence of a distant third body. We present three representative models of the hierarchical triple system and we numerically model the gravitational waveform. The motion of the bodies is simulated in the Newtonian approximation on a long timescale so that Lidov-Kozai oscillation can occur. This oscillation causes periodic exchange between relative incli- nation and eccentricity of the inner binary. We analyze the frequency spectrum of the waveform and identify the effect of perturbations on a timescale similar to the binary orbital period Tin, perturbations related to the orbital period of the third body Tout, and Lidov-Kozai cycles with an approximate period T2 out/Tin. It is expected that the upcoming space detector LISA (Laser Interferometer Space Antenna) will be able to detect these gravitational signals and it will be possible to derive information about the triple system from the waveform. 1
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Dynamics of spinning test particles in curved spacetimes
Zelenka, Ondřej ; Loukes Gerakopoulos, Georgios (advisor) ; Witzany, Vojtěch (referee)
The motion of a test particle in the Schwarzschild background models the merger of a compact object binary with extremely different masses known in the literature as Extreme Mass Ratio Inspiral. In the simplest geodesic approxima- tion, this motion is integrable and there is no chaos. When one takes the spin of the smaller body into account, integrability is broken and prolonged resonances along with chaotic orbits appear. By employing the methods of Poincaré surface of section, rotation number and recurrence analysis we show for the first time that there is chaos for astrophysically relevant spin values. We propose a uni- versal method of measuring widths of resonances in perturbations of geodesic motion in the Schwarzschild spacetime using action-angle-like variables. We ap- ply this novel method to demonstrate that one of the most prominent resonances is driven by second order in spin terms by studying its growth, supporting the expectation that chaos will not play a dominant role in Extreme Mass Ratio Inspirals. Last but not least, we compute gravitational waveforms in the time- domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source. 1
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Gravitational waves in cosmology
Kadlecová, Alžběta ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In this work, we study the backreaction of high-frequency gravitational waves on cosmological backgrounds. To describe the wave, we use the Isa- acson formalism, specifically the WKB approximation, which allows us to express the backreaction through an effective stress-energy tensor of the gra- vitational wave. First, we consider the inhomogeneous cosmological model of Charach and Malin, which contains gravitational waves and a massless scalar field mini- mally coupled to gravity. We show that although this is a spatially compacti- fied solution, it is possible to add a high-frequency perturbation and solve Einstein's equations with the effective stress-energy tensor in a consistent way. The bacreaction is of the same order as the influence of the scalar field. Second, we add multiple incoherent high-frequency waves to the homoge- neous Kasner background, and discuss the relation to the late-time limit of the Gowdy (vacuum Charach and Malin) model. 1
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Impulsive gravitational waves
Karamazov, Michal ; Švarc, Robert (advisor) ; Podolský, Jiří (referee)
In the review part of this bachelor thesis, we summarize various results about solutions to Einstein's gravitational field equations which describe both non-expanding and expanding impulsive gravitation waves in spacetimes of constant curvature. Special attention will be paid to geodesic motion in these spacetimes and to geometrical methods of their construction. In the original part of the thesis, we check compatibility of a direct solution to geodesic equation in (anti-)de Sitter spacetime with non-expanding impulsive wave and refraction formulae derived under the assumption of continuity of geodesics in a specific coordinate system. We also investigate an interaction of test particles with expanding spherical impulsive wave propagating on the Minkowski background which is generated by a pair of perpendicular snapping cosmic strings. Powered by TCPDF (www.tcpdf.org)
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Interaction of gravitational radiation with matter
Tintěra, Tomáš ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In the present work we study gravitational waves in the approximation of high frequency, and their interaction with matter waves with comparable frequency. We generalize the formalism of R. A. Isaacson to the case of non-vacuum spacetimes. We formulate and study a technique of so called averaging, which helps us to separate slow changes and high-frequency fluctuations of various tensor fields. The described methods are used in examples with a given particular metric - so called background metric. We thus study the interaction of high-frequency gravitational waves on the Robinson- Trautman background and the high-frequency electromagnetic waves. Further, we seek a perfect fluid with high-frequency energy-momentum tensor that could coexist with high-frequency gravitational waves on the flat Friedmann-Lemaˆıtre-Robertson-Walker background; again, we examine the relation between those potential gravitational and matter waves.
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Study of Exact Spacetimes
Švarc, Robert
In this work we study various aspects of the behaviour of free test particles in Einstein's general relativity and analyze specific physical properties of the background spacetimes. In the first part we investigate geodesic motions in the four-dimensional constant curvature spacetimes, i.e., Minkowski and (anti-)de Sitter universe, with an expanding impulsive gravitational wave. We derive the simple refraction formulae for particles crossing the impulse and describe the effect of nonvanishig cosmological constant. In the second part of this work we present a general method useful for geometrical and physical interpretation of arbitrary spacetimes in any dimension. It is based on the systematic analysis of the relative motion of free test particles. The equation of geodesic deviation is rewritten with respect to the natural orthonormal frame. We discuss the contributions given by a specific algebraic structure of the curvature tensor and the matter content of the universe. This formalism is subsequently used for investigation of the large class of nontwisting spacetimes. In particular, we analyse the motions in the nonexpanding Kundt and expanding Robinson--Trautman family of solutions.
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