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Electromagnetic Waves in Dispersiveand Refractive Relativistic Systems
Bezděková, Barbora ; Bičák, Jiří (advisor) ; Heyrovský, David (referee)
Study of light rays (light world lines) plays a significant role in many of astro- physical applications. Light rays are mainly studied in terms of so-called grav- itational lensing. However, the majority of studies are mainly focused on light propagation in vacuum. If the refractive and dispersive medium characterised by refractive index n is considered, effects occurring due to the medium presence need to be taken into account, which significantly complicates the problem. In the present thesis, rays propagating through simple refractive and dispersive systems, such as plane differentially sheared medium, are studied. In order to simplify the problem, the Hamiltonian equations of motion are used. The ray trajectories in the vicinity of Kerr black hole as well as accessible regions for the rays are also studied. Radial variation of the medium velocity is considered. Due to the recent increase of publications focused on the gravitational lensing in plasma, a detailed review summarizing the results obtained recently is included. 1
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Electromagnetic Waves in Dispersiveand Refractive Relativistic Systems
Bezděková, Barbora ; Bičák, Jiří (advisor) ; Heyrovský, David (referee)
Study of light rays (light world lines) plays a significant role in many of astro- physical applications. Light rays are mainly studied in terms of so-called grav- itational lensing. However, the majority of studies are mainly focused on light propagation in vacuum. If the refractive and dispersive medium characterised by refractive index n is considered, effects occurring due to the medium presence need to be taken into account, which significantly complicates the problem. In the present thesis, rays propagating through simple refractive and dispersive systems, such as plane differentially sheared medium, are studied. In order to simplify the problem, the Hamiltonian equations of motion are used. The ray trajectories in the vicinity of Kerr black hole as well as accessible regions for the rays are also studied. Radial variation of the medium velocity is considered. Due to the recent increase of publications focused on the gravitational lensing in plasma, a detailed review summarizing the results obtained recently is included. 1
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Motion of extended bodies in gravitational fields
Veselý, Vítek ; Žofka, Martin (advisor) ; Tahamtan, Tayebeh (referee)
In the first chapter of this thesis we analyse the problem of a dumbbell body moving in a homogeneous field and a central gravitational field. In the homogeneous field the centre of mass of the body behaves like a point particle regardless of the force acting between the two parts of the body if we introduce an additional external force to the equations of motion. A similar method is applied to the problem of a dumbbell body in a central gravitational field. We verify the results found by Burov and Kosenko [2015] and show that the orbiting body follows Kepler's second law of motion as well as a modification of the third law. We also show that the body can keep any orientation if its length is adjusted properly and we find two numerical solutions of such cases. In the second chapter we study the problem of an oscillating dumbbell body falling into a Schwarzschild black hole as proposed by Guéron and Mosna [2007]. We verify their results and study the velocity of the body after the maneuver and the case of high and low frequencies. Furthermore, we show that the body can continue to slow its fall by further oscillations.
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