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Astrophysical black holes embedded in organized magnetic fields
Karas, Vladimír
Large-scale magnetic fields pervade the cosmic environment where the astrophysical black holes are often embedded and influenced by mutual interaction. In thiscontribution, we outline the appropriate mathematical framework to describe magnetized black holes within General Relativity, and we show several examples of how these can be employed in the astrophysical context. In particular, we examine the magnetized black hole metric in terms of an exact solution of electro-vacuum Einstein-Maxwell equations under the influence of a non-vanishing electric charge. New effects emerge: the expulsion of the magnetic flux out of the black-hole horizon depends on the intensity of the imposed magnetic field.
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Thermodynamics of spacetime: A new perspective from the quantum realm
Liška, Marek ; Alonso Serrano, Ana (advisor) ; Oriti, Daniele (referee)
The main result of the thesis is the derivation of quantum phenomenological gravi- tational dynamics from the thermodynamics of local causal diamonds. By taking into account logarithmic corrections to entropy implied by quantum gravity effects, we derive new gravitational equations of motion which incorporate quantum corrections. The re- sulting theory appears to be a direct generalisation of the classical unimodular gravity instead of the general relativity. Upon obtaining the equations, we discuss their prop- erties and possible implications. As by-products, we also present a novel derivation of the Einstein equations from the thermodynamics of causal diamonds and a derivation of the logarithmic corrections to black hole entropy from the existence of minimal re- solvable area. Apart from the new results, we also provide an extensive review of the thermodynamics of local causal horizons. 1
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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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Teorie relativity - jak na středoškolské úrovni rozvíjet její pochopení
Ryston, Matěj ; Dvořák, Leoš (advisor) ; Novotný, Jan (referee) ; Šlégr, Jiří (referee)
The goal of this doctoral thesis is to find and implement possible ways to facilitate secondary school students' understanding of relativity. The thesis starts with an overview of existing literature as well as ongoingstudies concerned with teachingrelativityto secondarystudents, especially in connection with possible misconceptions and other learning difficulties. Furthermore, it maps available book and internet sources on relativity in both Czech and English that students might use outside of school. A research of Czech curricular documents for upper secondaryeducationandan online surveyamonggymnasium physics teachers were used to assess the current situation of teaching relativity in these schools. Based on the mentioned research, it was decided to develop learning resources focused on General Relativity. Following an analysis of a selection of relativity textbooks on this topic, a study website for interested students as well as a teaching-learningsequence for teachers to adapt in their own teaching were developed. The development and assessment of these materials are described in detail.
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Transition from regular to chaotic motion in black hole magnetospheres
Kopáček, Ondřej ; Karas, Vladimír (advisor) ; Kulhánek, Petr (referee) ; Rezzolla, Luciano (referee)
Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in...
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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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Geometry inside deformed black holes
Basovník, Marek ; Semerák, Oldřich (advisor) ; Svítek, Otakar (referee)
In this thesis we study exact general relativistic space-times generated by a black hole and an additional source of gravity, while restricting to two classes of static and axially symmetric solutions: the Majumdar-Papapetrou solution for a couple (in general, a multiple system) of extremally charged black holes and the "superposition" of a Schwarzschild black hole with the Bach-Weyl thin ring. We follow the effect of the additional source on the geometry of black-hole space-time on the behaviour of important invariants, in particular of the simplest scalars obtained from the Riemann and possibly also Ricci tensor. We have plotted the invariants both outside and inside the black hole; in the case of a Schwarzschild black hole with ring, we found, to this end, an extension of the metric below the horizon. It turns out that the external source may affect the geometry inside the black hole considerably, even in the vicinity of singularity, although the singularity itself remains point-like in both solutions studied here.
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Chaotic Motion around Black Holes
Suková, Petra ; Semerák, Oldřich (advisor) ; Šubr, Ladislav (referee) ; Loukes-Gerakopoulos, Georgios (referee)
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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Solving test-particle equations of motion near a black hole
Ryston, Matěj ; Ledvinka, Tomáš (advisor) ; Suková, Petra (referee)
Bachelor thesis Matěj Ryston 2011/2012 Abstract in English This work aims to give a well-arranged summary of the description and solving the equations of motion of particles outside a black hole (a star) with emphasis on numerical solutions. For that purpose a summary of numerical methods for solving ordinary differential equations, together with a review and comparison of chosen methods, is given. In the second chapter follows a brief recall of the foundations of General Relativity as well as the description of the geometry of Schwarzschild solution of the Einstein equations. After that equations of motion are formulated. In conclusion, selected numerical methods are used on solving said equations of motion of a test particle or those describing bending of light rays in closeness to a black hole.
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Modeling the Mach's principle in the post-Minkowskian approximation to general relativity
Schmidt, Tibor ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
The aim of this thesis is the simulation of relativistic phenomena in post- Minkowskian approximation. In the introduction the terms of Mach principle and gravitomagnetism are presented. Afterwards the principles of numeric solution of ordinary differential equations are summarized. Consequently, we get acquainted with the first post-Minkowskian approximation in canonical formalism and with elementary examples of its use. In the next chapter the results of performed simulations of classical General Relativity tests are described. The last chapter is devoted to the simulation of gravitomagnetism and of the system of rotating particles.
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