|
|
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.
|
|
|
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.
|
|
|
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)
|
|
|
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.
|
|
|
Spinning particles in algebraically special space-times
Šrámek, Milan ; Semerák, Oldřich (advisor) ; Krtouš, Pavel (referee)
Spinning-particle motion is studied, within the pole-dipole approximation, in algebraically special space-times of type N, III and D. The spin-curvature interaction is analysed for the Pirani and Tulczyjew spin supplementary conditions; for N and D types, the condition is related to a relative acceleration of two near observers separated in the direction of particle's spin. For Tulczyjew's condition, the momentum-velocity relation is also studied as well as its consequences for the spin-curvature interaction. Finally, the type of motion is mentioned for which both the supplementary conditions considered are equivalent.
|
|
|
Chaotic Motion around Black Holes
Suková, Petra ; Semerák, Oldřich (advisor) ; Šubr, Ladislav (referee) ; Loukes-Gerakopoulos, Georgios (referee)
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.
|
|
|
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)
|
|
|
Dark matter
Vraštil, Michal ; Mészáros, Attila (advisor) ; Heyrovský, David (referee)
The dark matter constituting approximately 85% of the mass is an integral part of our universe. As many astronomical observations at different scales of space so the theoretical models show that there is more matter than we can see directly. This overview describes the major historical events and observational data from the time of Zwicky to the present leading to today's view on the dark matter. The paper further describes the cosmological implications of the presence of dark matter - its impact on the formation of structures in the universe and reflection of fluctuations in the cosmic background radiation. Here I describe possible candidates for dark matter - a small contribution of baryonic matter and the main candidates among non-baryonic matter. In addition to possible new particles explaining the missing mass I describe alternatives to the theory of gravity, which do not require any extra matter, in particular, I deal with a very successful theory of MOND. At the end I mention a brief overview of today's possibilities of direct or indirect observation of dark matter.
|
|
|
Principles of gravitational-wave detection
Přeučil, Filip ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
In the present work we investigate the impact of weak gravitational wave in the linearized theory of gravity on a simple model of an interferometric gravitational wave detector, whose individual parts (mirrors, and electromagnetic field) are idealised by free test particles. After a necessary, fairly popularly conceived introduction to gravitational wave theory in the linearized gravity, the astrophysical sources of the gravitational waves, the possibilities of their detection and the principles of the detectors, we provide a mathematical survey of the indispensable parts of general relativity and of the linearized theory of gravity. After that, we finally deal with the model itself. In the linear approximation with respect to the perturbations, we solve the equations of motion of the individual components and derive the detector response to a gravitational wave. Finally, we present a few comments, including a proof of gauge invariance of the derived formula.
|
|
|
Properties of the extreme charged black hole near horizon
Hejda, Filip ; Krtouš, Pavel (advisor) ; Svítek, Otakar (referee)
It is known, that there exists a limiting correspondence between certain part (including the horizon) of extremal case of Reissner-Nordström space-time and Robinson-Bertotti space-time and that different generalisations of this near-horizon limit are possible. The aim of the presented work is to examine some of the properties of such limiting transitions. Firstly it is stressed how the global structure is reflected in the limit and secondly which properties of the space-time do provide that physical distances are preserved in the limit. Besides the extremal case the subextremal and hyperextremal generalisations are studied. As a complementary topic, the global extremal limit is stated. That means a transition from a generalised (non-symmetrical) conformal diagram of the subextremal case to the conformal diagram of the extremal case of Reissner-Nordström solution.
|
guest ::
