La mécanique statistique des systèmes auto-gravitants constitue un des plus fascinants et mystérieux champs de recherche. À cause de la nature à longue-portée de la force gravitationnelle, la notion usuelle d'équilibre statistique est modifiée, faisant de cette étude un problème hors-équilibre. Par conséquent, ces systèmes exhibent certaines propriétés particulières comme, par exemple, l'existence de transitions de phase associées à un effondrement gravitationnel. Le travail présenté dans cette thèse a comme but une description détaillée des transitions de phase dans un cadre général relativiste en considérant, en particulier, le cas des fermions auto-gravitants. La thèse est conceptuellement divisée en trois parties, selon le niveau de dégénérescence du système. D'abord, nous focalisons notre attention sur le cas des fermions dégénérés (T = 0), en étudiant en détail l'équilibre gravitationnel. Ensuite, en considérant la limite de haute température (T >> 1), nous montrons l'existence de deux types d'effondrement gravitationnel dans les séries d'équilibre. Enfin, nous explorons le cas général, en illustrant la présence des transitions de phase gravitationnelles, soit dans l'ensemble micro-canonique soit dans l'ensemble canonique. / The statistical mechanics of self-gravitating systems constitutes one of the most fascinating and puzzling fields of research. Due to the long-range nature of the gravitational force, the usual notion of statistical equilibrium is modified, making of this study an out-of-equilibrium problem. As a consequence, these systems exhibit some peculiar features such as the occurrence of phase transitions associated with a gravitational collapse. The work presented in this thesis aims at providing a detailed description of the phase transitions in a general relativistic framework by considering, in particular, the case of self-gravitating fermions. The thesis is conceptually divided in three parts, according to the degeneracy level of the system. We firstly focus our attention on the case of degenerate fermions (T = 0), by studying in detail the gravitational equilibrium. Successively, considering the high temperature limit (T >> 1), we show the existence of two kinds of gravitational collapse in the series of equilibria. Finally, we explore the general case, by illustrating the occurrence of the gravitational phase transitions, in both microcanonical and canonical ensembles.

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...

In recent years, more and more efforts have been expended on the study of $n$-dimensional asymptotically anti-de Sitter spacetimes $(\mathcal{M},g)$ as solutions to the Einstein vacuum equations \begin{align*} \mathrm{Ric}(g)=\frac{2}{n-2}\Lambda\, g \end{align*} with negative cosmological constant $\Lambda$. This has been motivated mainly by the conjectured instability of these solutions. The author of this thesis joins these efforts with two contributions, which are themselves independent of each other. In the first part, we are concerned with a superradiant instability for $n=4$. For any cosmological constant $\Lambda=-3/\ell^2$ and any $\alpha < 9/4$, we find a Kerr-AdS spacetime $(\mathcal{M},g_{\mathrm{KAdS}})$, in which the Klein-Gordon equation \begin{align*} \Box_g\psi+\frac{\alpha}{\ell^2}\psi=0 \end{align*} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound $r_+^2 > |a|\ell$. We obtain an analogous result for Neumann boundary conditions if $5/4 < \alpha < 9/4$. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses $\alpha$ such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result provides the first rigorous construction of a superradiant instability for a negative cosmological constant. In the second part, we study perturbations of five-dimensional Eguchi-Hanson-AdS spacetimes exhibiting biaxial Bianchi IX symmetry. Within this symmetry class, the Einstein vacuum equations are equivalent to a system of non-linear partial differential equations for the radius $r$ of the spheres, the Hawking mass $m$ and $B$, a quantity measuring the squashing of the spheres, which satisfies a non-linear wave equation. First we prove that the system is well-posed as an initial-boundary value problem around infinity $\mathcal{I}$ with $B$ satisfying a Dirichlet boundary condition. Second, we show that initial data in the biaxial Bianchi IX symmetry class around Eguchi-Hanson-AdS spacetimes cannot form horizons in the dynamical evolution.

The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial conditions. Observationally and theoretically this is a very ambitious task and therefore, current developments have been restricted to spherically symmetric dust models while only relaxing the usual assumption of homogeneity in the radial direction. These restricted models are important for the development of theoretical foundations and also useful as verification models since they avoid the circularity of verifying what has already been assumed. The work presented in this thesis is the development of such a model where numerical relativity (NR) is used to simulate the observable universe. Similar to the work of Ellis and co-workers [36], a reference frame based on the PNC is used. The reference frame used here, however, is based on that of the characteristic formalism of NR, which has developed for calculating the propagation of gravitational waves. This provides a formalism that is well established in NR, making the use of existing algorithms possible. The Bondi-Sachs coordinates of the characteristic formalism is, however, not suitable for calculations beyond the observer apparent horizon (AH) since the diameter distance used as a radial coordinate becomes multi-valued when the cosmological PNC reconverges in the history of a universe, smaller in the past. With this taken into consideration, the Bondi-Sachs characteristic formalism is implemented for cosmology and the problem approaching the AH is investigated. Further developments address the limitations approaching the AH by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced with an affine parameter. The model is derived with a cosmological constant Λ incorporated into the EFEs where Λ is taken as a parameter of the theory of gravity rather than as a matter source term. Similar to the conventional characteristic formalism, this model consists of a system of differential equations for numerically evolving the EFEs as a characteristic initial value problem (CIVP). A numerical code implemented for the method has been found to be second order convergent. This code enables simulations of different models given identical data on the initial null cone and provides a method to investigate their physical consistency within the causally connected region of our current PNC. These developments closely follow existing 3D schemes developed for gravitational wave simulations, which should make it natural to extend the affine CIVP beyond spherical symmetric simulations. The developments presented in this thesis is an extended version of two papers published earlier.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-09T19:22:16Z No. of bitstreams: 1 CAMILLA DOS SANTOS RODRIGUES LEITE – DISSERTAÇÃO (PPGFísica) 2012.pdf: 1293712 bytes, checksum: 38858a36d1603d9c94c3a7861fe88368 (MD5) / Made available in DSpace on 2018-10-09T19:22:16Z (GMT). No. of bitstreams: 1 CAMILLA DOS SANTOS RODRIGUES LEITE – DISSERTAÇÃO (PPGFísica) 2012.pdf: 1293712 bytes, checksum: 38858a36d1603d9c94c3a7861fe88368 (MD5) Previous issue date: 2012-05 / Capes / Uma caracterização bem elaborada das propriedades físicas das galáxias é de fundamental importância para entendermos o comportamento do Universo. Por outro lado, um dos grandes desafi os da Teoria da Relatividade Geral é encontrar soluções exatas com clara interpretação física. Nosso trabalho visa obter soluções exatas das equações de Einstein que possam representar modelos de discos galácticos, seguindo um método indireto para evitar a árdua tarefa de resolver as equações de Einstein diretamente. Para tanto, consideramos a ideia de uma hipersuperfície imersa em um espaço de dimensão superior, e utilizamos o formalismo da imersão associado ao Método "deslocar, cortar e refletir" (que pode ser considerado como uma adaptação do conhecido método das imagens, estudado em eletrostática), com o qual "cortando" e "colando" soluções conhecidas de vácuo, geramos soluções com fonte do tipo disco. Este procedimento é aqui denominado método da imersão, e constitui-se como uma ferramenta e ciente na modelagem de discos, visto que permite uma maior liberdade quanto à escolha da hipersuperfície de corte, e a consequente determinação das propriedades físicas (densidade, pressão, etc) do disco de matéria gerado. Este método, portanto, torna-se mais abrangente, uma vez que o método convencional se limita à analise de hipersuperfícies "planas", nas coordenadas consideradas. Através da aplicação desse método, verifi camos que o conteúdo material de um disco galáctico, idealizado como um disco de matéria infinitamente fino, é descrito por um tensor energia-momento super ficial cujas componentes podem ser escritas explicitamente em termos das funções de imersão. Estudando alguns casos particulares, reproduzimos os resultados encontrados na literatura. / The study of the physical properties of galaxies is very important to understand the behavior of the Universe. On the other hand, one of the great challenges of the General Theory of Relativity is to nd exact solutions which have a clear physical interpretation. Our work aims to obtain exact solutions of Einstein's equations that can represent models of galactic disks, by following an indirect method to avoid the di cult task of solving Einstein's equations directly. To this end, we consider the idea of a hypersurface embedded in a space of higher dimension, and we use the embedding formalism associated with the method of "displace", cut and reflect" (which can be considered as an adaptation of the known method of images, studied in electrostatics) on known vacuum solutions in order to generate solutions with disklike sources. This procedure, called the Embedding Method, is an e cient tool for modeling disks, as it allows great freedom in the choice of cutting hipersurfaces, and the consequent determination of physical properties (density, pressure, etc.) of the matter in the disk which is generated. Therefore, this method becomes more general than the conventional formulation of the method of "displace, cut and reflect", which works only to "plane" hypersurfaces (as viewed in the employed coordinate system). By applying the embedding formalism, we found that the material content of galactic disks, idealized as a in nitely thin disk of matter, is described by an energy-momentum tensor whose components can be written explicitly in terms of the embeeding functions. By studying individual cases, we reproduce some disk models found in the literature.

RODRIGUES, Joyce Mota. Entre telescópios e potes de barro: O eclipse solar e as expedições científicas em 1919/Sobral-CE. 2012. 133f. – Dissertação (Mestrado) – Universidade Federal do Ceará, Programa de Pós-graduação em História, Fortaleza (CE), 2012. / Submitted by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2013-10-11T11:19:45Z No. of bitstreams: 1 2012-DIS-JMRODRIGUES.pdf: 2543894 bytes, checksum: a2a82ca5560d8cf6847c270518012867 (MD5) / Approved for entry into archive by Márcia Araújo(marcia_m_bezerra@yahoo.com.br) on 2013-10-11T13:12:05Z (GMT) No. of bitstreams: 1 2012-DIS-JMRODRIGUES.pdf: 2543894 bytes, checksum: a2a82ca5560d8cf6847c270518012867 (MD5) / Made available in DSpace on 2013-10-11T13:12:05Z (GMT). No. of bitstreams: 1 2012-DIS-JMRODRIGUES.pdf: 2543894 bytes, checksum: a2a82ca5560d8cf6847c270518012867 (MD5) Previous issue date: 2012 / This research seeks to understand the daily routine of British, American and Brazilian Expeditions, in 1919, in the city of Sobral, in an attempt to confirm the Theory of Relativity by Albert Einstein. The relationships developed between scientists, local authorities and the media expose the discourses and scientific practices of modernity and backwardness local. / Esta pesquisa procura entender o cotidiano das Expedições Britânica, Americana e Brasileira, no ano de 1919, na cidade de Sobral, na tentativa de confirmar a Teoria da Relatividade de Albert Einstein. As relações travadas entre cientistas, autoridades locais e imprensa explicitam os discursos e as práticas científicas contrastantes de modernidade universal e atraso local.

MENDES, Wendel Macedo. Localização de Férmions em D dimensões. 2013. 55 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-23T19:20:31Z No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-23T19:38:03Z (GMT) No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) / Made available in DSpace on 2015-10-23T19:38:03Z (GMT). No. of bitstreams: 1 2013_dis_wmmendes.pdf: 369040 bytes, checksum: cd60b4ab7c07a63351d2b9dd5a277139 (MD5) Previous issue date: 2013 / In this work we analyzed the localization of fermions of spin-1/2 in a D-dimensional bulk in a (D-2)-branes scenario. The model used for this is a dimensional extension of models Randall-Sundrum (RS) and thick branes. It is known as co-dimension 1 model. The obtained results are based in no-factorizable geometry type Anti-de Sitter. During the zero mode localization process, it is uses both the Randall-Sundrum metric as a metric with smooth warped factor that depends on the coordinate of extra dimension, frequently used in thick brane models. As the spin-1/2 representations change with dimension of spacetime, the localization process, somehow, must take into account the dimensionality of bulk. Based on these models, one finds that the localization fermions in (D-2)-branes changes when the spacetime is par or odd. They are not located when the dimensionality of bulk is par an only one of chiralities can be located when D is odd. / Nesse trabalho é analizado a localização de férmions de spin 1/2 em um bulk D-dimensional em um cenário de (D-2)-branas. O modelo usado para tal é uma extensão para mais dimesões dos modelos Randall-Sundrum (RS) e de brana espessa. Ele é conhecido como modelo de codimensão 1. Os resultados obtidos são fundamentados em uma geometria não-fatorizável do tipo Anti-de Sitter. Durante o processo de localização do modo zero, usa-se tanto a métrica de Randall-Sundrum como uma métrica com fator de dobra suave que depende da coordenada da dimensão extra, frequentemente usada nos modelos de brana espessa. As representações de spin 1/2 variam com a dimensão do espaço-tempo, então o processo de localização deve levar em conta a dimensionalidade do bulk. Baseados nesses modelos, descobre-se que a localização de férmions em (D-2)-branas muda quando o espaço-tempo é par ou ímpar. Eles não são localizados quando a dimensionalidadedo bulk é par e somente uma das quiralidades pode ser localizada quando D é ímpar.

Este trabalho é a narrativa de uma experiência didática de aplicação de um módulo que abordou um tópico de Física Moderna e Contemporânea, a Teoria da Relatividade Restrita, no Ensino Médio. A proposta foi aplicada em uma escola particular situada no município de Arroio do Meio, RS, em uma turma de terceira série do nível médio regular, sob o referencial teórico da teoria cognitiva de Jean William Fritz Piaget (1896-1980) e sob o referencial epistemológico de Thomas Samuel Kuhn (1922-1996). Descreve-se o planejamento das aulas, a implementação da proposta e os resultados obtidos com sua aplicação em sala de aula na modalidade de um curso extraclasse. A forma como o módulo foi pensado e o nível de profundidade que foi possível alcançar aparecem ao longo do texto, que também oferece uma revisão da literatura em que a relevância da inclusão da Física Moderna e Contemporânea no currículo do Ensino Médio é discutida. Os resultados indicam que é possível trabalhar tópicos de Física Moderna e Contemporânea no ensino regular, que os alunos apreciaram e mostraram disposição para aprender assuntos atuais e que o esforço para introduzir pequenas atualizações curriculares é válido e precisa ser incentivado como uma das possíveis alternativas para se alcançar a melhoria de qualidade de ensino na Educação Básica. Ao final, um produto educacional em formato de texto de apoio, orientação e motivação aos professores de Física é apresentado. / This work is the narrative of a didactic experience of application of a module that addressed a topic of Modern and Contemporary Physics, the Special Theory of Relativity, in High School. The proposal was applied in a private school located in the county of Arroio do Meio, RS, for one group of third grade of regular secondary level, under the theoretical framework of cognitive theory of Jean William Fritz Piaget (1896-1980) and under the epistemological framework of Thomas Samuel Kuhn (1922-1996). It describes the planning of classes, the implementation of the proposal and the results obtained from its application in the classroom in the form of an extracurricular course. The way the module has been designed and the level of depth that was achieved is discussed throughout the text, which also provide a review of the literature in which importance of inclusion of Modern and Contemporary Physics in High School curriculum is discussed. The results indicate that it is possible teach subjects of Modern and Contemporary Physics in regular education. The results also indicated that students enjoyed and showed willingness to learn current issues and the effort to introduce small curriculum updates is valid and needs to be encouraged as one of the possible alternatives to achieve the improvement of teaching quality in basic education. At the end, an educational product in form of text, guidance and motivation to physics teachers is presented.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta dissertação, procuramos soluções exatas das equações de campo de Einstein em Relatividade Geral que descrevem um fluido perfeito em um espaço-tempo estático com simetria esférica. A técnica utilizada para encontrar essas soluções é o algoritmo de Kovacic, que pode ser aplicado a equações diferenciais ordinárias lineares e homogêneas de segunda ordem com coeficientes racionais. Esse algoritmo é capaz de nos dar soluções fechadas em termos de funções liouvillianas, se tal equação tiver esse tipo de solução. Para esse fim, vários sistemas de coordenadas foram investigados até encontrar o que fosse mais adequado à aplicação do algoritmo. Impondo que a função da métrica 11 g seja racional, ficamos com uma equação diferencial linear e homogênea de segunda ordem que tem coeficientes racionais. Nesse trabalho, as formas arbitradas foram: g11=-A/4x x-z1/x-Z1, g11=-A/4x x-z1/(x-Z1)(x-Z2), g11=-A/4x (x-z1) (x-z2)/x-Z1 e g11= -A/4x (x-z1) (x-z2)/ 4x(x-Z1) (x-Z2) onde x é uma coordenada espacial da métrica e &#913;, z1 , z2 , Z1 e Z2 são parâmetros dos modelos. Depois de obter soluções analíticas, verificamos se elas satisfazem determinadas condições físicas e, então, poderiam ser utilizadas como modelos de estrelas de nêutrons sem rotação (estrelas de alta densidade).

Neste trabalho foi feito um estudo do limite de Karlhede para ondas pp. Para este fim, uma revisão rigorosa de Geometria Diferencial foi apresentada numa abordagem independente de sistemas de coordenadas. Além da abordagem usual, a curvatura de uma variedade riemanniana foi reescrita usando os formalismos de referenciais, formas diferenciais e espinores do grupo de Lorentz. O problema de equivalência para geometrias riemannianas foi formulado e as peculiaridades de sua aplicação é a Relatividade Geral são delineadas. O limite teórico de Karlhede para espaços-tempo de vácuo de tipo Petrov N foi apresentado. Esse limite é estudado na prática usando técnicas espinores e as condições para sua existência são resolvidas sem a introdução de sistemas de coordenadas. / In this work a study of the Karlhede limit was made. To this end, a thorough review of Differential Geometry was presented in a coordinate independent approach. Besides the usual approach, the curvature of a riemannian manifold was rewritten using the formalisms of frames, differential forms and Lorentz group spinors. The equivalence problem for riemannian geometries was formulated and the peculiarities of its application to General Relativity are outlined. The theoretical Karlhede limit for vacuum Petrov N space-times is presented. This limit was studied in practice using spinor techniques and the conditions for its existence are solved without introducing coordinate systems.