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I have developed a technique to solve for the khronon field in a space-time containing a slowly moving black hole in the khrono-metric regime of Hořava Gravity. To develop these solutions I first revisited the khronon field around static spherically symmetric black holes and perturbed them by a small velocity. The equations of motions of the perturbed field were identified along with the linearly dependent series expansions at the boundary points. Using the boundary conditions and equations of motion the khronon field was numerically solved throughout the space-time. These solutions were used to calculate a sensitivity parameter which defines how the black hole mass appears to be modified due to its velocity. It was found that the sensitivity parameters are highly suppressed and black holes should appear similar to their general relativity counterpart. / Thesis / Master of Science (MSc) / I have investigated slowly moving black holes in a theory of modified gravity. The goal was to see whether the theory breaks down in modelling these black holes and if not, is it possible to test the theory using these predictions. I ultimately found that this theory can model the slowly moving black holes and would appear almost indistinguishable from classically moving black holes. This means that slowly moving black holes on their own will not provide a sufficient test of the theory.

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京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20907号 / 理博第4359号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 國友 浩, 教授 高柳 匡, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices. The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.

In this thesis we investigate selection effects in astrophysical observations. We demonstrate that the determination of the quasar black hole mass function and Eddington ratio distribution via observations are biased. By modelling the quasar selection function and the black hole mass measurement process we show that one is able to infer the true distribution of physical quantities from observations. We present the intrinsic accretion rates of AGN, the intrinsic accretion rates and the black hole mass function for optically selected quasars up to redshift of two. The results show that the Eddington limit continues to be a real physical limit to black hole accretion. We present a new upper limit of black hole masses from the inferred intrinsic black hole mass function and demonstrate the need of a mass dependent accretion rate in accordance with down sizing. Finally we investigate correlations between radio luminosity and observed black hole mass for optically selected quasars. We first show that mixing of fiat and steep spectrum quasars leads to results that are dependent on the observing frequency, and therefore should be treated with caution. We demonstrate that beaming of the radio core together with an orientation dependent optical selection effect can give rise to a bimodal distribution in the radio luminosities of optically selected quasars.

Following the financial turmoil in 2007/2008 liquidity black holes (LBH) has become arising topic often discussed among academics as well as portfolio managers all around the world. More recent view on liquidity risk covers those liquidity black holes which occur when the liquidity completely dries up in a particular market and the market becomes one-sided. There are basically 2 channels through which liquidity can be affected - Demand and Supply. In first case, the portfolios of investors lose the value and consequently the investors lose confidence in financial system. In the second case, banks hit their capital constraints, they tighten the terms of providing credits and loans to reduce the credit risk exposure and hence it becomes more difficult for firms to raise the funds. At this point dangerous spiral arises and the liquidity of financial system evaporates rapidly. The crucial point of this master thesis is to find the main determinants of Liquidity Black holes and find possible solutions to avoid their appearance.

O estudo de perturbações em buracos negros tem sido um campo de pesquisa ativo nas últimas décadas, levando a importantes contribuições para o entendimento da física de corpos compactos em geral. Para o caso de geometrias esféricas assintoticamente planas quadridimensionais, existe um panorama muito bem delineadi para a dinâmica de diversos campos de interesse. A introdução de uma constante cosmológica nas equações de Eisntein muda o caráter assintótico das soluções tipo buraco negro e neste caso, muito menos é conhecido. No trabalho desenvolvido nesta tese abordamos alguns aspectos da propagação de campos em geometrias esféricas assintoticamente de Sitter e anti-de Sitter, considerando inclusive geometrias com dimensão maios que quatro. No regime quase extremo a dinâmica é mais simples. Neste caso, são obtidas expressões analíticas para os potenciais efetivos e para os modos quase-normais, caracterizando completamente a dinâmica. Em geral, entretando, somos forçados a recorrer a métodos semi-analíticos e numéricos. Empregamos estes métodos para uma análise ampla da forma de decaimento dos diversos campos. Nossos resultados esboçam um quadro geral bastante coeso em uma grande gama de situações. / The study of pertubations in Black holes hás been na active Field of research in the last decades, leading to a better understanding of the physics of compact objects in general. In the case of asymptotically flat spherical geometries with four dimensions, there is a schematic Picture regarding the dynamics of many fields of interest. The introduction of a cosmological Constant in the Einstein equations changes the asymptotic character of the Black hole solutions, and in this case much less is known. In the work developed in this thesis we treat some aspects of the fiels propagation in spherically symmetric geometries which are asymptotically de Sitter and anti-de Sitter, considering also geometries with dimension greater than four. In the near extreme regime the dynamics is simpler. In this case, we obtain analytic expressions to the effective potentials and to the quasinormal modes, completely characterizing the dynamics. In general we are forced to use semi-analytics and numerical methods.These methods are employed in na extensive analysis of the decay modes of the fields cosidered. Our results sketch a general Picture in a wide sample of situations.