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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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Representation of dynamical black hole spacetimes in numerical simulations
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Hilditch, David (referee) ; Liebling, Steven L. (referee)
Choptuik's unexpected discovery, almost 30 years ago, of critical behavior in grav- itational collapse opened a whole new research area within numerical relativity. While critical collapse in spherical symmetry has been thoroughly investigated and is reasonably well understood, progress for axial symmetry has been much slower. In this thesis, we study axially symmetric gravitational collapse of gravi- tational waves using numerical simulations. We construct several very different initial data families and investigate their behavior close to the threshold of collapse. We compare them against each other and also against other published results. We use invariant quantities to look for signs of self-similarity and universality.
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Replacement of singularities in static spacetimes
Došek, Jan ; Ledvinka, Tomáš (advisor) ; Žofka, Martin (referee)
This bachelor thesis deals with the possibility of using the variational principle in the se- arch for internal solutions replacing singularities in static spacetimes. In the first instance, the thesis introduces the problematics on the simple case of classical Newton's gravity, where it also shows its practical application on several simple examples of symmetric potentials, and then it tries to generalize the theory for Einstein's gravity. It turns out that the relativistic problem could be loosely related to the so-called quadratic gravity as the internal solution is being found as a minimizer of a functional composed of quadrates of the Ricci tensor, the Weyl tensor and scalar curvature. Subsequently, it is verified that the newly presented theory in the newtonian limit yields the same results as the classical one. Finally, the thesis deals with the use of this theory to find an internal solution replacing the singularity in Schwarzschild spacetime and discusses its properties. 1
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Archaic, Traditional Law and Modern Commercial Law: A Study of Their Comparisons
Ledvinka, Tomáš ; Sokol, Jan (advisor) ; Kandert, Josef (referee) ; Brezina, Peter (referee)
The old anthropological question of the comparison between an archaic or traditional commercial law on one hand and a modern commercial law on the other is revisited using a conceptualization of an empirical study of legal comparisons performed within the real decision-making processes at work in the current Czech justice system. Commercial law is represented by a single legal institution - the law of reciprocity (comitas gentium) - which regulates the cooperation between various legal authorities and legal systems potentially entangled in cross-border commercial disputes. The reader is first introduced to the context and evidence-dependency of any legal comparison ranging from the representation of law and feud in Yemen at an asylum trial, to the legal systems regulating exchange contracts in Afghanistan involving cross-border disputes. The idea of comparing legal systems as two autonomous social units is abandoned in favor of the study of the comparative practices of a small population of Czech legal authorities, which furnishes readers with plenty of questions about the social organization of legal cognition. The dissertation refrains from drawing final conclusions using legal comparisons, instead it focuses on the limitations and barriers of marshalling evidence (symbolic representations) of...
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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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Beahvior of the solutions to the wave equation in compactified hyperboloidal slicing
Ivánek, Richard ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
In this bachelor thesis we discuss the effects of compactification and hyperboloidal slicing of spacetime in the numerical solution of wave equation primarily for their appli- cation in numerical relativity. The aim was to find the pros and cons of these concepts, to illustrate expected problems using diagrams and to rate the results obtained in spe- cific model problems. A brief explanation and demonstration of relevant numerical me- thods, hyperbolic Cauchy hypersurfaces, compactification and causal diagrams is a part of the thesis. As a conclusion, the effect of compactification and slicing on the accuracy of differential and integrational schemes was compared as well as the effect of discrete representation on the quality of initial data. 1
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