|
|
Space-times of ring sources
Pešta, Milan ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
Marginally outer-trapped surfaces (MOTSs) are found for a family of space-like hypersurfaces described by the Brill-Lindquist initial data. These hypersurfaces contain a singular ring characterized by its radius, mass and charge. Due to the ring character of the singularity, these surfaces are natural candidates for MOTSs with toroidal topology. By adjusting and employing the numerical method of geodesics, we indeed localize MOTSs of both spherical and toroidal topology, and compare the results with those obtained previously by Jaramillo & Lousto.
|
|
|
Physical interpretation of special solutions of Einstein-Maxwell equations
Ryzner, Jiří ; Žofka, Martin (advisor) ; Ledvinka, Tomáš (referee)
V klasické fyzice m·že být ustavena statická rovnováha v soustavě, která obsahuje extrémně nabité zdroje gravitačního a elektromagnetického pole. Udivujícím faktem je, že tato situace m·že nastat i pro černé díry v relativis- tické fyzice. Tato práce vyšetřuje speciální případ nekonečně dlouhé, extrémně nabité struny, zkoumá geometrii prostoročasu, elektrogeodetiky, vlastnosti zdroje a srovnává řešení se situací v klasické fyzice. Dále se zabýváme analogickou situací v dynamickém prostoročase s kosmologickou konstantou, a řešení porovnáváme s jeho statickou verzí. Nakonec zkoumáme periodické řešení Laplaceovy rovnice, které odpovídá nekonečně mnoha extremálním bodovým zdroj·m rozloženým v pravidelném rozestupu podél přímky. Vyšetřujeme vlastnosti elektrostatického potenciálu a ukazujeme, že v limitě velké vzdálenosti od osy tvořené zdroji pře- chází toto řešení v nabitou strunu. 1
|
|
|
Model of relativistic spinning system
Slezák, Daniel ; Ledvinka, Tomáš (advisor) ; Loukes Gerakopoulos, Georgios (referee)
Contrary to massive point particles, a description of extended bodies dynamics inclu- des higher mass moments, the first of which is spin. In this manner, Mathisson- Papapetrou-Dixon (MPD) equations has to be used instead of the geodesic equation to capture the more complicated evolution of the system. In this work, an extended system is represented by a set of freely moving, occasionally colliding point particles. As an aid in the construction of the model, some of these particles carry negative mass so it is possible to enclose their trajectories by elastic collisions. We then define a system's representative quantities, such as mass, momentum and spin. However, their relativistic theory requires to solve mainly the problems of parallel transport and the choice of a reference frame. Finally - from the known movement of the in- dividual particles, we can show that the whole system obeys the MPD equations. For that we use the simplification of small spacetime curvature along with a more extensive use of parallel transport instead of stress-energy tensor dynamic equation, the significance of which we limit to the behaviour of the component particles.
|
|
|
Gravitational collapse of magnetized matter
Bucko, Jozef ; Ledvinka, Tomáš (advisor) ; Scholtz, Martin (referee)
The scope of interest of this work is to study the gravitational collapse of magnetized matter. We consider homogeneous, isotropic and ideally conduct- ing star threaded by the test magnetic field. This field is chosen to be a relativistic generalization of dipole field outside the star and homogeneous field under the stellar surface. Dynamics of the collapse is described by Oppenheimer-Snyder solution so we consider the framework in which the motion of stellar matter re- mains unaffected by the magnetic field. In Schwarzschild's coordinates we review the exact solution of Maxwell's equations for electric and magnetic field inside the star and find the evolution equations for both fields outside the star that have to be treated numerically. Then we introduce Novikov coordinates and find the respective fields evolution equations. We test the equations using known exact so- lution for time-dependent magnetic dipole. Finally, we adopt chosen coordinates to become singularity-avoiding and integrate the respective differential equations numerically. 1
|
|
|
Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee) ; Gürlebeck, Norman (referee)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
|
|
|
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...
|
|
|
Kinematics of particle collisions in the ergosphere of Kerr black hole
Skoupý, Viktor ; Ledvinka, Tomáš (advisor) ; Žofka, Martin (referee)
In the thesis we deal with an effect which can be used to extract energy from a rotating black hole, so-called collisional Penrose process. First we investigate the ways to find the equations of motion in the general relativity using Hamilto- nian. Then we examine the equations of motion and their consequences in several coordinate systems for the space-time in the vicinity of a rotating black hole. Fi- nally we look into ways to create a particle capable to escape to infinity with as big energy as possible using Compton scattering and annihilation. The biggest energy found is approximately 14 times the energy of the incoming particles. The efficiency decreases with the distance from the horizon and with the decreasing specific angular momentum of the black hole. 1
|
|
|
Rotating thin disc around a Schwarzschild black hole: properties of perturbative solution
Kotlařík, Petr ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In 1974, Will presented a solution for the perturbation of a Schwarzschild black hole due to a slowly rotating and light thin disc given in terms of a multipole expansion of the perturbation series. In a recently submitted paper, P. Čížek and O. Semerák generalized this procedure to the perturbation by a slowly rotating finite thin disc, using closed forms of Green functions rather than the multipole expansion. The method is illustrated there, in the first perturbation order, on the constant-density disc. In this thesis, we summarize, check and plot some of the obtained properties, and show how the presence of the disc changes the geometry of a horizon and the position of significant circular orbits. 1
|
|
|
Electromagnetic rotational superradiance
Bára, Václav ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
We show the scattering of electromagnetic radiation on a rotating cylinder and a rotating sphere using formalism of the vector spherical harmonics in this thesis. If a specific condition is satisfied then we can observe the rotational superradiance, phenomena originally discovered by Y. B. Zel'dovich in 1970s saying that the radiation can gain power by scattering on a rotating body. In this particular case there is an underlying principle of the rotational superradiance, the energy dissipation in the form of Joule heating created due to the induction of surface currents on the conductor. Superradiance can occur in the radiation scattering on the rotating black hole background, although there is no dissipation present. We summarize the results of scattering on the Kerr black hole from the literature, including an application called Black hole bomb, when the black hole is enclosed into a perfectly reflecting mirror. We show that for the lowest modes of the radiation at specific intervals the general relativity results can be approximated by scattering on the flat spacetime.
|
|
|
Gravitational collapse of scalar field
Šípka, Martin ; Ledvinka, Tomáš (advisor) ; Scholtz, Martin (referee)
In this thesis we study a critical collapse of a scalar field. We follow the work of [1] and create detailed and easy to understand figures and images describing the results and the phenomena observed during our calculations. We also try to give a detailed look at numerical methods used along with two ways of convergence testing. 1
|
guest ::
