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Exact spacetimes in modified theories of gravity
Karamazov, Michal ; Švarc, Robert (advisor) ; Podolský, Jiří (referee)
In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1
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Investigation of chaotic dynamical systems using the methods of Riemannian geometry
Matejov, Dávid ; Scholtz, Martin (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we investigate a chaos in dynamical systems described by the Hamilton function using a new geometric method. At first, necessary definitions and terms are introduced, like dynamical systems, Lyapunov ex- ponents and Poncaré sections. Subsequently we deal with the new geometric method (Horowitz et al., 2007), which predicts the stability of a system un- der consideration. An extensive part is devoted to the general relativity and spinor formalism, the Newman-Penrose formalism and the theory of optical scalars. In the computational part of the thesis, we investigate the pp-waves and chaotic behaviour of geodesics in this class of space-times. All calcula- tions are done in the Python programming language, so we the chapter on numerical calculations is included. 1
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Algebraically special spacetimes - geometrical properties
Kuchynka, Martin ; Pravdová, Alena (advisor) ; Švarc, Robert (referee)
In the thesis, we set out to study a certain class of algebraically special spacetimes in arbitrary dimension. These are the so-called spacetimes of Weyl and traceless Ricci type N. Our work can be divided into two parts. In the first part, we study general geometrical properties of spacetimes under consideration. In particular, we are interested in various properties of aligned null directions - certain significant null directions associated with algebraic structure of the Weyl and the Ricci tensor. Since the obtained results are of geometric nature, they are theory-independent and thus hold in Einstein's gravity as well as in its various generalizations. In the second part of our work, we apply these general results in the Einstein-Maxwell p-form theory, within which spacetimes of traceless Ricci type N emerge naturally as a part of a solution of the Einstein-Maxwell equations with a null Maxwell field. Powered by TCPDF (www.tcpdf.org)
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Astrophysical processes near a galactic centre
Hamerský, Jaroslav ; Karas, Vladimír (advisor) ; Kulhánek, Petr (referee) ; Janiuk, Agnieszka (referee)
An accretion torus is an important astrophysical phenomenon which is be- lieved to account for various features of mass inflow and release of radiation on diverse scales near stellar-mass as well as supermassive black holes. When the stationary torus is perturbed it starts to oscillate and once some part of the torus overflows the closed equipotential surface, defined by the stationary solution, this material is accreted or ejected. These oscillations reveal both spacetime properties and the intrinsic characteristics of the torus model. We study the oscillation and accretion properties of geometrically thick accretion tori using general relativistic magnetohydrodynamic simulations. Assuming axial symmetry these simulations are restricted to 2-D approximation. We discuss the impact of the presence of the large scale magnetic field and the profile of the specific angular momentum on the oscillation properties and on the accretion flow motion. 1
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Geodetic structure of multi-black-hole spacetimes
Ryzner, Jiří ; Žofka, Martin (advisor) ; Svítek, Otakar (referee)
V klasické fyzice m·že být ustavena statická rovnováha v soustavě nabitých hmotných bod·, jsou-li poměry náboje a hmotnosti každého hmotného bodu stejné. Udivujícím faktem je, že tato situace m·že nastat i pro černé díry v relativistické fyzice. Obecný případ takovéhoto systému poprvé popsali Majumdar a Papapetrou nezávisle na sobě v roce 1947. Tato práce se zabývá jeho speciálním případem obsahujícím dvě nabité černé díry, zkoumá elektrogeodetiky v tomto prostoročasu a srovnává je se situací v klasické fyzice. Dále též shrnujeme situaci v případě nestatického vesmíru, kterou popsali Kastor a Traschenová v roce 1992, a tuto geometrii srovnáváme se statickou verzí. 1
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Possibilities of teaching/learning general relativity at elementary level
Ryston, Matěj ; Dvořák, Leoš (advisor) ; Žák, Vojtěch (referee)
This thesis deals with an elementary introduction to general relativity on a level understandable by secondary school students and graduates. It contains a review of available literature including its approach to the introductory level of relativity, a study text covering the necessary parts of classical mechanics, special relativity and subsequently basic ideas and conclusions of general relativity. A didactical analysis of the study text is also part of the thesis. The text presumes only basic knowledge of secondary school physics (mostly mechanics), therefore it is suitable for a wide range of readers amongst secondary school students and graduates. It can also be useful as a study material for secondary school teachers, who wish to enrich their teaching with more modern chapters of physics.
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Cosmological constant
Bjelka, Jakub ; Mészáros, Attila (advisor) ; Křížek, Michal (referee)
The aim of this work is concentration of the relevant knowledges from area history of the cosmological constant. Theory listed in time sequence show its origin, evolution and problems associated with it. In this work are commented static models which are made possible by the existence of a cosmological constant. Parameters obtained from experiments BAO (baryon acoustic oscillations) from Supernova Type Ia measurements (SNe) and from measurements of the cosmic microwave background (CMB) are, as the marginal conditions determined also. Furthermore, there are commented alternative solutions of the problem of cosmological constant in the form of a cyclic model or time variable of the cosmological "constant". In conclusion, there is mentioned the possibility of alternative to cosmological constant in the form of quintescence.
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Chaotic Motion around Black Holes
Suková, Petra
As a non-linear theory of space-time, general relativity deals with interesting dynamical systems which can be expected more prone to chaos than their Newtonian counter-parts. In this thesis, we study the dynamics of time- like geodesics in the static and axisymmetric field of a Schwarzschild black hole surrounded, in a concentric way, by a massive thin disc or ring. We reveal the rise (and/or decline) of geodesic chaos in dependence on parameters of the sys- tem (the disc/ring mass and position and the test-particle energy and angular momentum), (i) on Poincaré sections, (ii) on time series of position and their power spectra, (iii) by applying two simple yet powerful recurrence methods, and (iv) by computing Lyapunov exponents and two other related quantifiers of or- bital divergence. We mainly focus on "sticky" orbits whose different parts show different degrees of chaoticity and which offer the best possibility to test and compare different methods. We also add a treatment of classical but dissipative system, namely the evolution of a class of mechanical oscillators described by non-standard constitutive relations.
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Superluminal motion in general relativity
Gattermann, Rico ; Ledvinka, Tomáš (advisor) ; Krtouš, Pavel (referee)
We show how superluminal travel can be achieved by means of the Alcubierre warp drive. In this spacetime a spaceship locally at rest is surrounded by a "bubble" moving faster than the speed of light. We derive the equations of motion for photons and massive particles and illustrate properties of their solutions. We will find that warp drives cause frequency shifts and refraction of light passing the bubble wall, which affects the view of the outside universe seen by a traveller on spaceship. As for superluminal warp drives, existence of horizons will be shown. We will discuss that the stress-energy tensor, generating a warp corridor in spacetime, is not related to any classical field or matter, and attempts to interpret it via quantum mechanics resulted in extreme amounts of matter required. Powered by TCPDF (www.tcpdf.org)
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Symmetries of systems in spaces related to high-dimensional black hole spacetime
Kolář, Ivan ; Krtouš, Pavel (advisor) ; Kubizňák, David (referee)
In this work we study properties of the higher-dimensional generally rotating black hole space-time so-called Kerr-NUT-(A)dS and the related spaces with the same explicit and hidden symetries as the Kerr-NUT-(A)dS spacetime. First, we search commuta- tivity conditions for classical (charged) observables and their operator analogues, then we investigate a fulfilment of these conditions in the metioned spaces. We calculate the curvature of these spaces and solve the charged Hamilton-Jacobi and Klein-Gordon equations by the separation of the variables for an electromagnetic field, which pre- serves integrability of motion of a charged particle and mutual commutativity of the corresponding operators.
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