Desenvolvemos aqui um estudo das formulações alternativas-equivalentes da Relatividade Geral, baseada no formalismo de conexões de Ashtekar. Iniciamos discutindo a estrutura matemática necessária de fibrados e conexões, e a teoria de sistemas Hamiltonianos vinculados. Em seguida, damos uma breve introdução ao formalismo métrico de Einstein e então passamos ao formalismo geometrodinâmico canônico (formalismo ADM). Introduzimos as transformações no espaço de fase que geram as formulações alternativas, de forma generalizada tal que possamos obter ambas as variáveis complexas de Ashtekar ou as variáveis reais de Barbero, ou mesmo qualquer forma intermediária por meio do parâmetro de Immirzzi. / We develop here a study of the alternative-equivalent formulations of General Relativity, based on Ashtekars connexion formalism. We begin discussing the mathematical structure needed of fibre bundles and connexions, and the theory of constrained Hamiltonian systems. Next, we give a brief introduction for Einsteins metric formalism and then we pass to the canonical geometrodynamic formalism (ADM formalism). We introduce the transformations of the phase space which generate the alternative formulations, in a generalized form such that we can obtain both Ashtekars complex variables or Barberos real variables, or even any intermediary form by using the Immirzzi parameter.

A presente dissertação revisa um modelo, de autoria de C. Dappiaggi, K. Fredenhagen e N. Pinamonti, de um campo escalar real quântico não-interagente acoplado com a métrica de um espaço-tempo FLRW (Friedmann-Lemaítre-Robertson-Walker). Apresentamos a metodologia de quantização de campos de Klein-Gordon reais em espaçostempos globalmente hiperbólicos e discorremos sobre o procedimento de regularização do tensor de energia-momento via point-splitting. Consideramos os campos em espaços FLRW e estados adiabáticos com flutuação média de campo dado por h2i = m2 +R, com ; constantes provenientes do procedimento de regularização. A retroação do campo quântico gera a equação diferencial para o parâmetro de Hubble H(t) dada por _H (H2H2 c ) = (H2H2+ )(H2H2 ) com Hc uma constante e H pontos críticos estáveis da equação. Esse simples modelo mostra que efeitos quânticos podem, por si só, fornecer fases de de Sitter estáveis sem adição de uma constante cosmológica a priori. Mesmo que de caráter apenas qualitativo, tal resultado indica que análises cautelosas de processos de quantização são importantes para análise de efeitos cosmológicos de teorias quânticas de campos em espaços curvos. / The present dissertation reviews the coupling of a scalar non-interacting quantum field with the metric of a FLRW(Friedmann-Lemaítre-Robertson-Walker) spacetime, proposed in a work by C. Dappiaggi, K. Fredenhagen and N. Pinamonti. We present methods for the quantization of a real Klein-Gordon field in globally hyperbolic spacetimes and discuss procedures for the point-splitting regularization of the stress-energy tensor. We consider those fields in FLRWspacetimes and point out adiabatic states with mean field fluctuation given by h2i = m2+R, with ; being constants that emerge from the regularization procedure. The backreaction of the quantum field provides a diferential equation for the Hubble parameter given by _H (H2H2 c ) = (H2H2+)(H2H2) with Hc a constant and H stable critical points of the equation. In this way, this simple model demonstrates that quantum efects may, by themselves, exibit stable de Sitter phases even without an introduction of a cosmological constant by hand. Althoug in a qualitative way, such result shows that, when dealing with the backreaction issue, a careful analysis of the quantization procedures is important for the analysis of cosmological efects of models of quantum field theories in curved spacetimes.

Neste trabalho faremos uma investigação no campo das perturbações gravitacionais e propagação de ondas em geometrias de buracos negros com campos elétricos ou magnéticos. Usando uma geometria tipo Ernst-Melvin de um buraco negro massivo em um Universo com campo magnético no eixo z, calculamos os modos quasi-normais de propagação de um campo escalar, demonstrando que este se comporta como um campo escalar com massa 2|m|B em uma geometria de Schwarzschild, para pequenos valores do campo magnético B (correspondendo m ao número azimutal do esférico harmônico). Ainda com esta geometria, calculamos a contribuição de ondas escalares para a entropia do buraco negro em termos dos cut offs ultravioleta e infravermelho. Com uma solução do tipo Reissner-Nordström em 4 dimensões, investigamos as possíveis correspondências entre os modos quasinormais e as propriedades termodinâmicas deste buraco negro, atestando o resultado de que a conjectura Hod modificada por Maggiore é válida em tal solução. Também, com uma geometria de Reissner-Nordström-de Sitter D-dimensional, obtivemos os modos quasi-normais de vibração para dois potenciais diferentes, estabelecendo a ausência de modos instáveis para uma grande gama de parâmetros deste buraco negro. / In this work we make an incursion into the branch of gravitational perturbations and field propagation around known-geometries of black holes with electromagnetic fields. Using an Ernst-Melvin type of geometry in a massive black hole immersed on a magnetic Universe, we calculate the quasi-normal modes of the propagating field, showing the equivalence of this problem with that of a massive scalar field (for which the mass is 2|m|B, m being the azhimutal number, and B the magnetic field) propagating around a Schwarzschild geometry. We also compute the contribution of the scalar field to the entropy of the black hole in terms of the infrared and ultraviolet cut offs. Using a Reissner-Nordstr¨om-like solution in 4 dimensions, we investigate the possible correspondence between quasi-normal modes and the thermodynamical properties of this black hole, atesting the validity of the modified Hod conjecture as proposed by Maggiore. Finally, for a Reissner-Nordstr¨om-de Sitter D-dimensional solution, we obtain the quasi-normal modes for two diferent potentials, establishing the absence of unstable modes for a large range of values for the black hole parameters.

Vladimir Aleksandrovich Fock est un physicien largement reconnu par la communauté scientifique pour ses contributions de premier plan aux théories de la mécanique quantique et de la relativité générale. Il est aussi un acteur majeur du débat sur l'interprétation de ces deux théories du XXe siècle, selon une approche qui se revendique clairement du matérialisme dialectique, une idéologie alors largement imposée par les autorités soviétiques en URSS. Notre étude porte principalement sur cet aspect de sa carrière, exploré jusqu'alors de façon trop partielle en histoire des sciences. Plus spécifiquement, nous nous penchons sur les racines scientifiques et philosophiques des interprétations non-orthodoxes des théories de la mécanique quantique et de la relativité générale que développe Fock. En reconstruisant son approche épistémologique nous mettons en évidence que le physicien est guidé par une vision antiréductionniste et réaliste scientifique de sa discipline. Cette base nous donne alors l'assise pour discuter des raisons pour lesquelles le matérialisme dialectique est une véritable influence pour la pensée du physicien soviétique. Par la suite, partant du constat de la sincère adoption par Fock de cette idéologie, nous replaçons la question de l'interprétation des théories de la physique moderne dans son contexte socio-culturel. Il est y notamment question d'observer le parcours du physicien en tant que défenseur des théories de la mécanique quantique et de la relativité face aux différentes attaques politiques et idéologiques qu'elles peuvent subir en Union soviétique, mais aussi d'étudier l'influence du contexte sur la formulation à proprement parler de leurs interprétations et dans un dernier temps de développer les questions relatives à la diffusion des idées de Fock dans la communauté locale et internationale des physiciens. En somme, cette thèse permet de reconsidérer l'intérêt que présente la pensée de Vladimir Aleksandrovich Fock dans l'histoire des théories de la physique moderne / Vladimir Aleksandrovich Fock is a physicist well-known by the scientific community for his important contributions to the theories of quantum mechanics and general relativity. He is also a major actor in the debate on the interpretation of these two major theories of the XXth century, following an approach that clearly claims dialectical materialism ñ an ideology then largely imposed by the Soviet authorities in the USSR - as fundamental. Our work mostly focuses on this aspect of Fock's career, explored too partially in the history of science. More specifically, we reconsider the scientific and philosophical roots of the non-orthodox interpretations of quantum mechanics and general relativity developed by Fock. By reconstructing his epistemological approach we put forward that the physicist was guided by an antireductionist and a scientific realist conception of his discipline. This basis gives us the possibility to discuss the reasons why dialectical materialism was a real influence on the scientist thought. Thus, by following the observation of the sincere adoption by Fock of the Soviet ideology, we put back the question of the interpretation of the theories of modern physics in its socio-cultural context. We observe Fock's trajectory as a defender of quantum mechanics and relativity theory against the different ideological and political attacks they may undergo in Soviet Union. We also study the influence of context on the actual wording of their interpretations and finally we develop the issues related to their diffusion in the local and worldwide community of physicists. To summarize, this thesis helps to reconsider the interest of Fock's thought in the history of modern physics

Orientador: Ricardo Pereira Tassinari / Banca: Osvaldo Frota Pessoa Júnior / Banca: Marcelo Carbone Carneiro / Resumo: Esta Pesquisa se insere na área de Epistemologia Genética. O objetivo geral desta Pesquisa é discutir as estruturas necessárias ao conhecimento da Teoria da Relatividade Restrita de Albert Einstein segundo o Modelo do Sistema de Esquema de Ações e Operações sobre Símbolos e Signos (MoSEAOSS), um modelo baseado na Epistemologia Genética de Jean Piaget. Com vista a esse objetivo, são objetivos específicos desta Pesquisa: discutir os fenômenos da dilatação dos tempos e da contração dos comprimentos consequentes dos postulados da Teoria da Relatividade Restrita, assim como o Paradoxo dos Gêmeos, e, com base neles, analisar a noção de espaço-tempo que deles resultam; apresentar o MoSEAOSS, assim como os principais conceitos nele envolvidos, em especial, os conceitos de transfiguração e de transignação; aplicar o MoSEAOSS à Teoria da Relatividade Restrita e mostrar que a noção de espaço-tempo pode ser explicada por meio de operações que o sujeito realiza sobre símbolos e signos. / Abstract: This research is in the area of Genetic Epistemology. The overall goal of this research is to discuss the necessary structures for knowing Albert Einstein's Special Theory of Relativity according to the Model of the System of Schemes of Actions and Operations on Symbols and Signs (MoSEAOSS), a model based on Jean Piaget's Genetic Epistemology. The specific objectives of this research are: to discuss the phenomena of Time Dilation and Length Contraction that follow the postulates of Special Theory of Relativity, as well as the Twin Paradox, and, based on them, to analyze the notion of space-time that results from them; to introduce the MoSEAOSS, as well as the key concepts involved in it, especially, the concepts of transfiguration and transignation; to apply the MoSEAOSS to Special Theory of Relativity and to show that the notion of space-time can be explained by means of operations that the subject performs on symbols and signs. / Mestre

From Birkoff's theorem, the geometry in four spacetime dimensions outside a spherically symmetric and static, gravitating source must be given by the Schwarzschild metric. This metric therefore satisfies the Einstein vacuum equations. If the mass which gives rise to the Schwarzschild spacetime geometry is concentrated within a radius of r=2M, a black hole will form. Non-accelerating particles (freely falling) traveling through this geometry will do so along parametrized curves called geodesics, which are curved space generalizations of straight paths. These geodesics can be found by solving the geodesic equation. In this thesis, the geodesic structure in the Schwarzschild geometry is investigated with an attempt to generalize the solution to higher dimensions.

Abstract not available

We use standard general relativity to clarify common misconceptions about fundamental aspects of the expansion of the Universe. In the context of the new standard Lambda-CDM cosmology we resolve conflicts in the literature regarding cosmic horizons and the Hubble sphere (distance at which recession velocity equals c) and we link these concepts to observational tests. We derive the dynamics of a non-comoving galaxy and generalize previous analyses to arbitrary FRW universes. We also derive the counter-intuitive result that objects at constant proper distance have a non-zero redshift. Receding galaxies can be blueshifted and approaching galaxies can be redshifted, even in an empty universe for which one might expect special relativity to apply. Using the empty universe model we demonstrate the relationship between special relativity and Friedmann-Robertson-Walker cosmology. We test the generalized second law of thermodynamics (GSL) and its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the relative entropic &quoteworth&quote of black hole versus cosmological horizon area. An intriguing set of models show an apparent entropy decrease but we anticipate this apparent violation of the GSL will disappear when solutions are available for black holes embedded in arbitrary backgrounds. Recent evidence suggests a slow increase in the fine structure constant over cosmological time scales. This raises the question of which fundamental quantities are truly constant and which might vary. We show that black hole thermodynamics may provide a means to discriminate between alternative theories invoking varying constants, because some variations in the fundamental &quoteconstants&quote could lead to a violation of the generalized second law of thermodynamics.

This thesis reports on the recent results of a continuing, high-precision pulsar timing project, currently focused on the nearby, binary millisecond pulsar, PSR J0437_4715. Pulse arrival time analysis has yielded a remarkable series of constraints on the physical parameters of this system and evidence for the distortion of space-time as predicted by the General Theory of Relativity. Owing to the proximity of the PSR J0437_4715 system, relative changes in the positions of the Earth and pulsar result in both annual and secular evolution of the line of sight to the pulsar. Although the changes are miniscule, the effects on the projected orbital parameters are detectable in our data at a high level of significance, necessitating the implementation of an improved timing model. In addition to producing estimates of astrometric parameters with unparalleled precision, the study has also yielded the first three-dimensional orbital geometry of a binary pulsar. This achievement includes the first classical determination of the orbital inclination, thereby providing the unique opportunity to verify the shape of the Shapiro delay and independently confirm a general relativistic prediction. With a current post-fit arrival time residual RMS of 130 ns over four years, the unrivaled quality of the timing data presented herein may eventually contribute to the most stringent limit on the energy density of the proposed stochastic gravitational wave background. Continuing the quest for even greater timing precision, a detailed study of the polarimetry of PSR J0437_4715 was undertaken. This effort culminated in the development of a new, phase-coherent technique for calibrating the instrumental response of the observing system. Observations were conducted at the Parkes 64-m radio telescope in New South Wales, Australia, using baseband recorder technologies developed at York University, Toronto, and at the California Institute of Technology. Data were processed off-line at Swinburne University using a beowulf-style cluster of high-performance workstations and custom software developed by the candidate as part of this thesis.

[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.