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Termodynamika černých děr. Entropie a informace.
Liška, Marek ; Acquaviva, Giovanni (advisor) ; Scholtz, Martin (referee)
The aim of the thesis is to provide a review of black hole thermodynamics and its relation with concepts of entropy and physical information. We start by deriving the four laws of black hole thermodynamics in the context of classical general relativity. To supplement this, we use semiclassical limit of quantum mechanics to show that black holes radiate and have non-zero thermodynamic temperature. In the second part of the thesis we describe the concepts of the Shannon and von Neumann entropy and of physical information. Lastly, we discuss the use of these concepts in the context of black hole mechanics. 1
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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.
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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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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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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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Exact spacetimes in modified theories of gravity
Karamazov, Michal ; Švarc, Robert (advisor)
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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Study of geodesic chaos by fractal methods
Sychrovský, David ; Semerák, Oldřich (advisor) ; Čížek, Martin (referee)
We study the dynamics of free test particles in a field of Schwarzschild black hole surrounded by an external exact thin axisymmetric solutions of Einstein's equations. Specifically, we use the Bach-Weyl ring and two member of the inverted Morgan-Morgan family of solutions as the additional sources. The fractal basin boundary and other meth- ods are used to detect and quantify chaos in time-like geodesic motion of the particles, primarily by computing box-counting dimension of said basin boundary. Our results mainly consist of the dependence of the chaoticity of these systems on mass and radius of the additional source as well as conserved energy and angular momentum of the test particles. We compare our results to literature and expand on them. 1
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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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Physical interpretation of special solutions of Einstein-Maxwell equations
Ryzner, Jiří ; Žofka, Martin (advisor)
In Newtonian physics, it is possible to establish static equilibrium in a system, which consists of extremal sources of gravitational and electromagnetic field. Surprisingly, this situation can occur in general relativity for black holes, too. This work examines a special case involving an infinitely long, straight, extremally charged string, studies its geometry, electrogeodesics, properties of the source and compares the solution to Newtonian physics. We also investigate an analogous situation in a dynamic spacetime with cosmological constant, and we compare it to the static version. Finally, we investigate a periodical solution of Laplace's equation corresponding to infinitely many extremal point sources distributed at regular intervals along a straight line. We study the properties of the electrostatic potential and show that in the limit of large distances from the axis formed by the sources, the solution approaches the charged string. 1
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Numerical solution of the Ernst equation
Pospíšil, Marek ; Ledvinka, Tomáš (advisor) ; Svítek, Otakar (referee)
This work is concerned with solving the Ernst equation using numerical techniques, namely pseudospectral methods. In theoretical chapters, we summarize the properties of some black-hole space-times. The work then cites the derivation of the Ernst equation and the Kerr solution. Afterwards we present pseudospectral techniques on the example of a numerical solution of the Laplace equation with a boundary condition at infinity. Finally we solve a non-linear differential equation, thus proving, that pseudospectral methods might be used even on the Ernst equation. 1
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