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Elastic strings in general relativity
Frühauf, Josef ; Žofka, Martin (advisor) ; Tahamtan, Tayebeh (referee)
We study a simple model of a one dimensional extended body in a gravitational field, consisting of two point particles connected by an elastic string, and derive equations of motion for this system in both classical mechanics and general relativity. We study the motion of the system with a focus on the relationship between these models, and the difference of its motion from geodesic. 1
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Nonlinear Electrodynamics
Hale, Tomáš George ; Tahamtan, Tayebeh (advisor) ; Žofka, Martin (referee)
Nonlinear electrodynamics, introduced in the 1930s to remedy divergences associated with Maxwell's theory, has become a recurring theme in theoret- ical physics. Recent developments in the area of nonlinear electrodynamics coupled to gravity have prompted the creation of an accessible ground up reformulation of the basic structure. We develop the formalism by building upon classical electromagnetism in Minkowski spacetime, deriving the funda- mental equations by the action principle before re-deriving the Lagrangians of two important models from the founding era and describing the corre- sponding regular static spherically symmetric solutions. The focus is then shifted to the examination of a recently discovered model through which we develop a basic background for the coupling of nonlinear electrodynamics to gravity and AdS black hole thermodynamics.
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Exact spacetimes and their physical properties
Veselý, Jiří ; Žofka, Martin (advisor) ; Hennigar, Robie (referee) ; Tahamtan, Tayebeh (referee)
Motivated by our desire to find generalizations of the Bonnor-Melvin spacetime, the thesis investigates seven static, cylindrically-symmetric and electrovacuum exact solutions to the Einstein-Maxwell equations. They contain a magnetic field and six of them also include the cosmological constant. After discussing some of the methods we use during our investigation, we present the basic properties of the spacetimes, and for each of them we also study charged test particle motion and their admissible shell sources composed of particle streams. We also perform numerical computations to determine whether the equations admit more general solutions than the exact ones we derived. 1
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Superradiance on accelerated systems
Žlábek, Martin ; Kofroň, David (advisor) ; Tahamtan, Tayebeh (referee)
In this work we will study the electromagnetic superradiance phenomenon on acceler- ated systems. We will briefly cover superradiance on a cylinder, which was thermodynam- ically proven by Zel'dovich. Then we will attempt to formulate the problem in accelerated coordinates, namely the flat-spacetime limit of the C-metric. Briefly introducing the C- metric, the Newman-Penrose formalism and the Geroch-Held-Penrose formalism along the way. Using the formalism of vector spherical harmonics, we point out the complica- tions which arise from not respecting the spherical symmetry of the spherical coordinate system. 1
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Properties of multi black-hole spacetimes
Klimešová, Eliška ; Žofka, Martin (advisor) ; Tahamtan, Tayebeh (referee)
In Newtonian physics, a system of extremally charged particles (electric charge equal to gravitational mass in geometrized units) remains in a static equilibrium until an external force is applied. This situation, surprisingly, translates exactly to general relativity in the case of extremely charged black holes, as was inde- pendently shown by Sudhansu Datta Majumdar and Achilles Papapetrou in 1947. Moreover, if the system is perturbed, giving the black holes small initial velocities vi ≪ c, it can be described by a metric first discussed by Robert Craig Ferrell and Douglas Michael Eardley in 1987. We examine whether it is possible to arrive at the perturbed metric in some special cases, such as boosting or spinning up the original static metric. We further study the case of two inter- acting black holes, which is equivalent to a classical mechanics problem with a special Lagrangian. We discuss the critical impact parameter separating cases of coalescing and scattering black holes as they spiral closer together from infinity. We find the critical value as a function of the ratio of the black holes' masses. Finally, we compare the limiting case where one of the holes is much heavier than the other to a trajectory of an extremally charged test particle in extremal Reissner-Nordstr¨om. 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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