Estudamos as restrições impostas pelo princípio da covariância sobre o procedimento de quantização em espaços planos e curvos. Mostramos que o conjunto de todas as quantizações covariantes em espaços planos em coordenadas retangulares é composto de ordenamentos de operadores de posição e momento e exibimos uma parametrização funcional deste conjunto. Deduzimos regras para a quantização covariante em espaços planos em coordenadas gerais. Generalizamos estas quantizações para espaços curvos e mostramos que nestes espaços, além da ambiguidade de ordenamento, surge uma nova ambiguidade relacionada à curvatura. Este novo tipo de ambiguidade explica o surgimento de uma classe grande de potenciais quânticos no problema da quantização de uma partícula não relativística em um espaço curvo. / We study the restrictions imposed by the covariance principle on the quantization procedure in flat and curved spaces. We show that the set of all covariant quantizations in flat spaces in rectangular coordinates is composed of position and momentum operator orderings and exhibit a functional parametrization of this set. We deduce rules for the covariant quantization in flat spaces in general coordinates. We generalize these quantizations for curved spaces and show that in such spaces, besides the ordering ambiguity, it appears a new ambiguity related to the curvature. This new kind of ambiguity explains the appearence of a wide class of quantum potentials in the problem of quantization of a non-relativistic particle in curved space.

In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in d dimensions with and without a cosmological constant.<p><p>The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions.<p><p>The second part of this thesis contains the original contributions.<p>Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure particularly transparent, and constitute the main original result of the thesis.<p>Secondly, asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner in $d$ dimensions. In agreement with a recent conjecture, a Virasoro-Kac-Moody type algebra is found not only in three dimensions but also in the four dimensional asymptotically flat case.<p><p>These two parts of the thesis are supplemented by appendices. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Orientador: Alberto Vazquez Saa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-22T06:52:24Z (GMT). No. of bitstreams: 1 Freitas_VanessaPachecode_M.pdf: 1200814 bytes, checksum: 8b3bfadc5901d2f7c992d013c3957d07 (MD5) Previous issue date: 2013 / Resumo: Podemos utilizar o conhecido m'etodo &quot;Deslocar, cortar e refletir¿ para construir soluc¿oes exatas das Equac¿oes de Einstein correspondentes 'a espacos-tempo com distribuic¿oes discoidais de materia. Esse metodo consiste na introduc¿ao de uma descontinuidade na primeira derivada do tensor metrico. O resultado é uma soluc¿ao com uma singularidade do tipo delta de Dirac na hipersuperficie z = 0. Nosso estudo se restringiu a discos finos estaticos utilizando as soluc¿oes de Schwarzschild e Gutsunaev-Manko, sendo esta a representac¿ao de um objeto massivo com configurac¿ao de campo magnetico com simetria dipolar. Incluiu-se tambem o estudo da estabilidade da orbita de particulas-teste no disco, generalizando os criterios de estabilidade de Rayleigh e uma segunda analise para testar a estabilidade do disco atraves de uma perturbac¿ao no tensor energia-momento. / Abstract: We can use the well-known &quot;Displace, cut and reflect¿ method to construct exact solutions of Einstein Equations that correspond to space-times with disklike distribution of matter. This method consists on the introduction of a discontinuity in the first-order derivative of the metric tensor. The result is a solution with a singularity of the Dirac delta type in the hypersurface Z = 0. Our study was restricted to static thin disks using Schwarzschild and Gutsunaev-Manko solutions, being the last the representation of a massive object with magnetic field configuration with dipolar symmetry. We include also the stability study of test-particles orbits at the disk, generalizing the Rayleigh criteria of stability and a second analysis to test the stability of the disk through a perturbation in the energy-momentum tensor / Mestrado / Física / Mestra em Física

Orientadores: Alberto Vazquez Saa, Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T13:28:54Z (GMT). No. of bitstreams: 1 Vieira_RonaldoSavioliSume_D.pdf: 9121576 bytes, checksum: eab8bcedfd86d048afd51f4b65fe9501 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho analisamos aspectos dinâmicos de sistemas astrofísicos que possuem uma componente discoidal proeminente. Estudamos o movimento de partículas de teste (estrelas) que cruzam discos galácticos bidimensionais e axialmente simétricos, obtendo uma fórmula para o envelope das órbitas que depende somente da densidade superficial $\Sigma$ do disco. Essa fórmula nos dá uma terceira integral de movimento aproximada para o sistema. Também analisamos a estabilidade das órbitas circulares equatoriais nesses discos, chegando à condição de estabilidade vertical $\Sigma>0$. Esse formalismo é estendido para discos tridimensionais, assim como para a relatividade geral (em que obtivemos que a \textit{condição de energia forte} é suficiente para a estabilidade vertical das órbitas circulares em discos infinitesimais, no caso estático e axialmente simétrico). Trabalhamos também com a aproximação pós-newtoniana (1PN), obtendo o formalismo hamiltoniano para uma distribuição arbitrária de matéria, assim como as correções 1PN nas frequências epicíclicas radial e vertical para configurações estacionárias e axialmente simétricas e a terceira integral de movimento aproximada para discos infinitesimais (estacionários). Outro resultado obtido foi a dependência das frequências epicíclicas com a curvatura riemanniana do espaço-tempo para distribuições suaves de matéria-energia, no caso estático e axialmente simétrico em relatividade geral. A segunda parte desta tese corresponde aos resultados para discos de acreção. Analisamos o movimento de partículas de teste na métrica de Kehagias & Sfetsos (solução esfericamente simétrica da gravitação de Horava no caso em que o espaço-tempo é assintoticamente plano), na região de parâmetros em que a singularidade central é nua. Por fim, estudamos a espessura dos discos de acreção super-Eddington obtida por simulações globais recentes de radiation magnetohydrodynamics em relatividade geral. O resultado foi comparado com modelos de discos slim para taxas de acreção similares, levando à conclusão de que o estado final (estacionário) dos fluxos de acreção gerados por essas simulações é um disco slim, e não um disco espesso, como seria esperado pelas características das configurações iniciais do tipo Polish Doughnuts usualmente adotadas / Abstract: In this work, we analyze dynamical aspects of astrophysical systems containing a prominent discoidal component. We study the motion of test particles (stars) which cross bidimensional, axially symmetric galactic disks, obtaining a formula for the orbits' envelope which depends solely on the disk's surface density. This formula gives us an approximate third integral of motion for the system. We also analyze the stability of equatorial circular orbits in these disks, arriving at the vertical stability condition $\Sigma>0$. This formalism is extended to three-dimensional disks, as well as to general relativity (in which we obtained that the \textit{strong energy condition} is sufficient for vertical stability of circular orbits in infinitesimal disks, in the static and axially symmetric case). We also worked with the post-Newtonian approximation (1PN), obtaining the Hamiltonian formalism for an arbitrary matter distribution, as well as the 1PN corrections to the radial and vertical epicyclic frequencies for stationary and axially symmetric configurations, and the approximated third integral of motion for (stationary) infinitesimal disks. Another result obtained was the dependence of the epicyclic frequencies on the Riemannian spacetime curvature for smooth matter-energy distributions, in the static and axially symmetric case. The second part of this thesis corresponds to the results concerning accretion disks. We analyzed the motion of test particles in the Kehagias & Sfetsos metric (spherically symmetric solution to Horava's gravity in the case in which the spacetime is asymptotically flat), in the parameter region in which the singularity is naked. Finally, we studied the thickness of super-Eddington accretion disks, obtained via recent global radiation magnetohydrodynamics simulations in general relativity. The result was compared with slim-disk models for similar accretion rates, leading to the conclusion that the final (stationary) state of accretion flows generated by these simulations is a slim disk, and not a thick disk, as it would be expected by the characteristics of the usually adopted Polish Doughnuts initial configurations / Doutorado / Física / Doutor em Ciências

Un des grand défis de la physique actuelle est la quantification de la gravit é. La théorie d’Einstein est remarquable pour ses prédictions. Malheureusement, elle reste une théorie classique et de ce fait en désaccord avec les progrès actuels en physique des particules qui montrent qu’à faible distance, une théorie physique doit être quantique. Une des pistes pour résoudre ce problème est d’étudier la version classique de la gravité dans l’espoir d’en déduire des propriétés ou même la forme de la théorie quantique.<p><p>Un des outils pour étudier une theorie est la notion de dualité. On dit que deux théories sont duales quand elles décrivent le même système par des moyens différents. La dualité est le dictionnaire permettant de passer d’une description à l’autre. Dans ma thèse, j’ai étudié deux dualités s’appliquant à la gravité en 4 dimensions.<p><p>La première est connue sous le nom de dualité électromagnétique. A l’origine, cette dualité s’applique à l’électromagnétisme où elle échange les rôles du champ & / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Despite the many successes of the current standard model of cosmology on the largest physical scales, it relies on two phenomenologically motivated constituents, cold dark matter and dark energy, which account for approximately 95% of the energy-matter content of the universe. From a more fundamental point of view, however, the introduction of a dark energy (DE) component is theoretically challenging and extremely fine-tuned, despite the many proposals for its dynamics. On the other hand, the concept of cold dark matter (CDM) also suffers from several issues such as the lack of direct experimental detection, the question of its cosmological abundance and problems related to the formation of structure on small scales. A perhaps more natural solution might be that the gravitational interaction genuinely differs from that of general relativity, which expresses itself as either one or even both of the above dark components. Here we consider different possibilities on how to constrain hypothetical modifications to the gravitational sector, focusing on the subset of tensor-vector-scalar (TeVeS) theory as an alternative to CDM on galactic scales and a particular class of chameleon models which aim at explaining the coincidences of DE. Developing an analytic model for nonspherical lenses, we begin our analysis with testing TeVeS against observations of multiple-image systems. We then approach the role of low-density objects such as cosmic filaments in this framework and discuss potentially observable signatures. Along these lines, we also consider the possibility of massive neutrinos in TeVeS theory and outline a general approach for constraining this hypothesis with the help of cluster lenses. This approach is then demonstrated using the cluster lens A2390 with its remarkable straight arc. Presenting a general framework to explore the nonlinear clustering of density perturbations in coupled scalar field models, we then consider a particular chameleon model and highlight the possibility of measurable effects on intermediate scales, i.e. those relevant for galaxy clusters. Finally, we discuss the prospects of applying similar methods in the context of TeVeS and present an ansatz which allows to cast the linear perturbation equations into a more convenient form.

Acompanha: Produto educacional: uma sequência didática para ensinar relatividade restrita no ensino médio com o uso de TIC / FUNPESQ / A Sequência Didática proposta neste trabalho contempla as recomendações dos Parâmetros Curriculares Nacionais (PCN), no sentido de uma progressiva inserção da Física do século XX no ensino médio, tema este que, infelizmente, ainda é muito pouco abordado nas salas de aula do país. O uso das Tecnologias de Informação e Comunicação (TIC) na educação pode proporcionar processos de educação mais participativos, tornando a relação professor‐aluno mais aberta e interativa. Com este intuito, o presente trabalho apresenta a aplicação de uma sequência didática, incluindo suas análises e resultados em sala de aula, para o ensino da Relatividade Restrita aos alunos do ensino médio de um Colégio da rede particular de ensino, no município de Apucarana-Pr. A proposta tem como base teórica a Aprendizagem Significativa de David Ausubel. A sequência em questão faz uso sistemático de recursos computacionais, com destaque para uma planilha original desenvolvida em Excel, com o propósito de melhorar o entendimento de conceitos básicos da Relatividade Restrita, bem como para a dedução de relações matemáticas fundamentais que são decorrência lógica dos postulados de Einstein. Além deste recurso, também foi utilizada a História da Ciência para contextualizar os alunos acerca do momento histórico em que o mundo estava inserido na época que a Teoria da Relatividade Restrita foi desenvolvida. Com isto, os alunos puderam ainda aprender um pouco sobre a vida, a obra e a contribuição deixada por Albert Einstein. Ainda foi utilizado um trecho do filme Interestelar que aborda a viagem no tempo, além de simuladores computacionais. Todos os recursos foram aplicados buscando aproximar a tecnologia (bem conhecida dos jovens) com a sala de aula, com o intuito de melhorar o processo de ensino-aprendizagem. Nossos resultados apontam que a utilização das TIC neste processo propiciam uma aula interativa e dinâmica tanto para o aluno quanto para o professor. Sendo assim, podemos dizer que a proposta aplicada possui um grande potencial pedagógico, pois os alunos, no decorrer da aplicação, mostraram-se mais motivados para as aulas de física. Acreditamos que esse seja o primeiro passo para que a aprendizagem ocorra de forma significativa. / The Didactic sequence proposed in this paper considers the recommendations of the National Curriculum Parameters (PCN), towards a gradual integration of twentiethcentury physics in high school, a topic that unfortunately is still very little explored in the country's classrooms. The use of Information and Communication Technologies (ICT) in education can provide more participatory education process, making it more open and interactive teacher-student relationship. To this end, this work presents the application of a didactic sequence, including its analysis and results in the classroom for teaching relativity to high school students of the College of private schools in the municipality of Apucarana- Pr. The proposal is based on theoretical Meaningful Learning of David Ausubel. The sequence in question is systematic use of computational resources, especially an original spreadsheet developed in Excel, in order to improve understanding of basic concepts of relativity, as well as the deduction of fundamental mathematical relationships that are logical consequence of the postulates Einstein. In addition to this feature, it was also used the History of Science to contextualize students about the historical moment in which the world was inserted at the time that the theory of relativity was developed. With this, students could still learn a little about life, work and contribution left by Albert Einstein. Interstellar a movie part that deals with time travel, and computer simulators also was used. All resources were applied seeking to approach the technology (well-known youth) in the classroom, in order to improve the teachinglearning process. Our results indicate that the use of ICT in this process provide an interactive lesson and dynamic for both the student and the teacher. Thus, we can say that the proposal applied has a great pedagogical potential as students, during the application, were more motivated to physics classes. We believe this is the first step in learning to occur significantly.

Cette thèse se consacre premièrement à certains aspects de la définition de charges conservées en relativité générale pour les espaces asymptotiquement plats à l’infini spatial. À l’aide de la dualité gravitationnelle, présente au niveau linéarisé, on étudie également l’existence de charges topologiques, magnétiques, ainsi que leurs contributions aux superalgèbres dans les théories de supergravité N = 1 et N = 2 à quatre dimensions. La thèse est divisée en trois parties.<p>Dans la première partie, les espaces asymptotiquement plats à l’infini spatial sont décrits à l’aide d’une généralisation de la métrique de type Beig-Schmidt. La construction de charges à partir de l’étude des équations du mouvement et de la classification de tenseurs symétriques et de divergences nulles nous permet de démontrer l’unicité des charges de Poincaré pour l’ansatz non-généralisé en présence de conditions de parité. L’équivalence des charges de Ashtekar- Hansen et Mann-Marolf est ainsi revisitée. Dans le cas d’un ansatz généralisé, une régulation de la forme symplectique divergente, à l’aide de contre-termes rajoutés à l’action de Mann-Marolf, nous donne la possibilité de considérer un espace des phases sans conditions de parité, tout en gardant un principe variationnel bien défini. Le groupe asymptotique comprend alors, en plus des charges de Poincaré où les charges de Lorentz ne sont plus asymptotiquement linéaires, des charges non-triviales associées aux supertranslations et aux transformations logarithmiques.<p>Dans la deuxième partie, on étudie la dualité gravitationnelle et la définition de charges magnétiques en gravitation linéarisée. On revisite la dualité et on montre qu’une dualisation sur les indices de Lorentz facilite la compréhension de celle-ci. Les dix charges de Poincaré ainsi que leurs duales magnétiques sont alors exprimées en termes d’intégrales de surface. Nous illustrons ensuite nos résultats à travers l’étude des sources de certaines solutions électriques et de leur duales magnétiques. Les solutions électriques envisagées sont :les trous noirs de type Schwarzschild et de type Kerr ainsi que les ondes de chocs de type pp.<p>Dans la dernière partie, on établit la supersymétrie des espaces de type Taub-NUT lorentzien chargés électriquement et magnétiquement dans la supergravité N = 2. Motivé par l’existence d’une égalité BPS, on entreprend alors une recherche sur l’inclusion de la charge NUT dans l’algèbre de supersymétrie. Grâce à une complexification de la forme de Witten-Nester, cette contribution de la charge NUT à la superalgèbre est comprise comme une déformation topologique, symétrique, au crochet antisymétrique des super-charges. Ce résultat est alors appliqué à la superalgèbre N = 1 à travers l’étude des ondes de chocs de type pp.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Depuis sa formulation au début du 20ème siècle, la théorie de la Relativité Générale a été vérifiée avec une précision sans cesse croissante. Cette théorie prédit, entre autre, l'existence d'ondes gravitationnelles qui restent à ce jour inobservées, et ce malgré de nombreuses tentatives de détections. Ces ondes sont caractérisées par leur absence de masse. Une des questions qui se pose alors est de savoir si cette absence de masse est une condition nécessaire pour que théorie et observations concordent. Pour répondre à cette question, il est indispensable d'étudier les différents aspects des théories décrivant des ondes gravitationnelles massives. Au-delà de cet intérêt purement théorique, l'étude de ces théories est, entre autre, motivée par de récentes observations cosmologiques. Celles-ci indiquent que l'accord entre la Relativité Générale et les observations n'est possible que si on suppose l'existence de matière et d'énergie noires.<p><p>Cette thèse est dédiée à une classe de théories décrivant des ondes gravitationnelles massives. Dans un premier temps, nous résumons les différents problèmes qui surgissent lorsqu'on tente de donner une masse aux ondes gravitationnelles. Ensuite, nous introduisons une classe de modèles et étudions certaines de leurs caractéristiques.<p><p>Le premier aspect étudié concerne l'existence d'une interaction de type instantanée. De telles interactions sont possibles étant donné que l'invariance de Lorentz est spontanément brisée dans les modèles considérés. Celles-ci sont dès lors discutées et un exemple concret est fourni.<p><p>La présence d'une interaction instantanée dans ces modèles a une conséquence directe sur les solutions "trous noirs" des équations du champ. En effet, on s'attend à ce que l'interaction instantanée puisse propager de l'information à l'extérieur d'un trou noir, ce qui entraînerait une modification de ces solutions par rapport à celles de la Relativité Générale. Cette supposition est confirmée par les solutions "trous noirs" obtenues dans cette thèse. Celles-ci peuvent soit imiter une certaine quantité de matière noire, soit conduire à un champ gravitationnel répulsif.<p><p>Finalement, les mécanismes de formation des grandes structures de l'Univers (galaxies, amas de galaxies, ) sont étudiés pour les théories considérées. Cette dernière discussion démontre que ces modèles reproduisent le comportement prévu par la Relativité Générale et sont, par conséquent, en accord avec les observations. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished