Orientador: Patricio Anibal Letelier Sotomayor / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T23:13:00Z (GMT). No. of bitstreams: 1 Manoel_JoaoPauloPitelli_M.pdf: 2107794 bytes, checksum: 5fe60d22c5d7bd4e165a24c4c9c6d375 (MD5) Previous issue date: 2008 / Resumo: Espaços-tempos classicamente singulares são estudados utilizando-se partículas quânticas (ao invés de clássicas) obedecendo as equações de Klein-Gordon e Dirac, a fim de determinar se estes espaços permanecem singulares do ponto de vista quântico. Primeiramente é apresentada uma revisão do ferramental matemático necessário para o estudo de singularidades quânticas, cujo principal resultado utilizado é a teoria de índices deficientes devido a von Neumann. No apêndice A é apresentado um primeiro estudo sobre singularidades quânticas em espaços-tempos com defeitos topológicos numa superfície 2-dimensional (paredes cósmicas), em especial superfícies esféricas e cilíndricas. Estes espaços continuam singulares nesta teoria e todas as informações extras (que em mecânica quântica se apresentam sob a forma de condições de contorno) necessárias para se remover a singularidade são encontradas. No apêndice B, é estudado um espaço-tempo 2+1 dimensional com curvatura negativa constante. É mostrado que este espaço permanece singular quando visto pela mecânica quântica e as condições de contorno possíveis são encontradas utilizando-se resultados obtidos no caso plano / Abstract: Classical singular spacetimes are studied using quantum particles (instead of classical ones) obeying Klein-Gordon and Dirac equations, to determine if these spacetimes remain singular in the view of quantum mechanics. First we give a review of the mathematical framework necessary to study quantum singularities, wich the main result to be used later is von Neumann¿s theory of deficient indices. In appendix A, a first work on quantum singularities in spacetimes with topological defects on a 2-dimensional hypersurface (cosmic walls), specifically spherical and cylindrical surfaces, is presented. These spacetimes remain singular in this theory and all extra informations (which in quantum mechanics correspond to boundary conditions) necessary to remove the naked singularity are found. In Apendix B, a 2+1 dimensional spacetime with constant negative curvature is studied. It is shown that this spacetime remains quantum mechanically singular and all possible boundary conditions are found using results obtained in plane case / Mestrado / Relatividade Geral/Gravitação Quantica / Mestre em Matemática Aplicada

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-12T14:56:03Z No. of bitstreams: 1 thiagomorallesdeabreu.pdf: 433339 bytes, checksum: dc2019985b911c7c131a86a07cac34de (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-15T13:36:51Z (GMT) No. of bitstreams: 1 thiagomorallesdeabreu.pdf: 433339 bytes, checksum: dc2019985b911c7c131a86a07cac34de (MD5) / Made available in DSpace on 2016-08-15T13:36:51Z (GMT). No. of bitstreams: 1 thiagomorallesdeabreu.pdf: 433339 bytes, checksum: dc2019985b911c7c131a86a07cac34de (MD5) Previous issue date: 2016-06-24 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Na presente dissertação é apresentada uma revisão detalhada de modelos cosmológicos, incluindo a dinâmica de perturbações cosmológicas lineares para dois modelos que desempenham interesse do ponto de vista de possíveis aplicações. Todo material discutido é oriundo da literatura recente e não se apresenta elementos originais. Entretanto, o conhecimento desses modelos abre uma possibilidade de extensões que estão agora sob discussão e desenvolvimento. De início é feita uma sucinta exposição do Modelo Cosmológico Padrão, que pode ser associado com o modelo FLRW (Friedmann-Lemaître-Robertson-Walker). Este último descreve um Universo em expansão marcado pela homogeneidade e isotropia em grande escala. Após isso discute-se o modelo com fluido cósmico composto por gás relativístico reduzido, mais conhecido pela sigla RRG, do inglês "reduced relativistic gas". A equação de estado do modelo RRG tem uma correspondência bem próxima ao modelo de gás de partículas massivas com energias cinéticas relativísticas. Considera-se ainda as perturbações cosmológicas em torno do modelo RRG de fundo plano, homogêneo e isotrópico. Por fim, segue-se a discussão sobre a possibilidade de incluir perturbações na constante gravitacional G e na constante cosmológica Λ, no ramo do modelo motivado por correções semiclássicas. / In this thesis we present a detailed review of some cosmological models, including the theory of linear cosmological perturbations for two distinct models which represent certain interest from the point of view of possible applications. All presented material comes from the recent literature and does not include original elements. However, the knowledge of these models opens a possibility of extensions which are now under discussion and development. At first it is presented a brief review of the Standard Cosmological Model, which can be associated with FLRW model (Friedmann-Lemaître-Robertson-Walker). The latter describes an expanding Universe marked by homogeneity and isotropy on a large scale. After that we discuss the model composite by a cosmic fluid described by reduced relativisticgas,betterknownbytheacronymRRG(reducedrelativisticgas). Theequation of state of the RRG model has a very close match to the model of gas of massive particles with relativistic kinetic energies. We consider the cosmological perturbations around the background of flat, homogeneous and isotropic RRG-based model. After that follows the discussion of the possibility of including perturbations of the gravitational constant G and the cosmological constant Λ within the model motivated by semiclassical corrections.

Le Modèle Standard de la cosmologie décrit la formation des structures à grande échelle dans l'Univers récent dans un cadre quasi–newtonien. Ce modèle requiert la présence de composantes inconnues, la Matière Noire et l'Énergie Noire, afin de vérifier correctement les observations. Ces deux quantités représentent à elles seules près de 95% du contenu de l'Univers. Bien que ces composantes sombres soient activement recherchées par la communauté scientifique, il existe plusieurs alternatives qui tentent de traiter le problème des structures à grande échelle. Les théories inhomogènes décrivent l'impact des fluctuations cinématiques sur le comportement global de l'Univers. D'autres théories proposent également d'aller au-delà de la relativité générale. Durant cette thèse, j'ai mis au point des éléments clés d'une théorie lagrangienne totalement relativiste de la formation des structures. Supposant un feuilletage particulier de l'espace–temps j'ai résolu le système d'équations du premier ordre afin d'obtenir des solutions décrivant l'évolution de la matière dans un espace à la géométrie perturbée. J'ai également développé un schéma de résolution pour les ordres supérieurs de perturbation ainsi que leurs équivalent newtoniens. Une autre partie de ce travail de thèse consiste en le développement de quelques applications directes : la description d'un Univers silencieux ou l'hypothèse de courbure de Weyl et le problème de 'entropie gravitationnelle. Les objectifs à plus ou moins court terme seraient d'obtenir la description d'observables physiques and le développement d'autres applications. Cette étape de développement sera une interaction entre approches théorique et numérique et requerra de se rapprocher fortement des observateurs / The standard model of cosmology describes the formation of large scale structures in the late Universe within a quasi–Newtonian theory. This model requires the presence of unknown compounds of the Universe, Dark Matter and Dark Energy, to properly fit the observations. These two quantities, according to the Standard Model, represent almost 95% of the content of the Universe. Although the dark components are searched for by the scientific community, there exist several alternatives which try to deal with the problem of the large scale structures. Inhomogeneous theories describe the impact of the kinematical fluctuations on the global behaviour of the Universe. Or some theories proposed to go beyond general relativity. During my Ph.D. thesis, I developed key–elements of a fully relativistic Lagrangian theory of structure formation. Assuming a specific space–time slicing, I solved the first order system of equations to obtain solutions which describe the matter evolution within the perturbed geometry, and I developed higher order schemes and their correspondences with the Lagrangian perturbation solutions in the Newtonian approach. I also worked on some applications of these results like the description of a silent Universe or the Weyl curvature hypothesis and the problem of gravitational entropy. Further objectives are the description of physical observables and the development of direct applications. Next step of the development is an interaction between theoretical and numerical approaches, a study which would require strong cooperation with observers

L'exactitude délivrée par les systèmes de positionnement globaux par satellites (GNSS) est un facteur clé pour de nombreuses applications scientifiques telles que le positionnement de points géodésiques ou d’autres satellites, l'établissement de systèmes de référence spatio-temporels, la synchronisation d’horloges ou encore l'étude directe du lien pour sonder l’atmosphère. L'augmentation de la constellation GNSS avec des mesures de pseudo-distances entre les satellites est une option prometteuse pour améliorer l'exactitude du système. Plusieurs études présentent l'apport qualitatif de ces liens inter-satellites (ISL), mais ne permettent pas de mesurer efficacement l'impact quantitatif de cette technologie. Dans cette thèse, nous avons effectué une étude différentielle entre un système classique (possédant seulement des liens standards espace-sol) et un système augmenté avec des ISL. Les deux systèmes sont étudiés sous les mêmes hypothèses et à travers le même code de calcul. Celui-ci est composé de deux parties distinctes et autonomes : une simulation d’observables sous la forme de pseudo-temps de vol bruités, et une analyse qui délivre, après ajustement des paramètres, les bilans d’erreurs quantitatifs. La comparaison des bilans d'erreurs quantitatifs associés aux deux systèmes nous permet d’établir, pour une même application donnée, les différences de performance relatives entre les deux systèmes. Les résultats obtenus permettent de franchir un pas de plus vers la validation de l’apport des liens inter-satellites et sont à considérer pour les versions futures des systèmes de navigation par satellites. / The accuracy reached by the Global Navigation Satellite Systems (GNSS) is critically important for many scientific applications such as geodetic point or satellite positioning, space-time reference frame realization, clocks synchronization or the study of the links to probe the atmosphere. One option for improving the system accuracy is the use of inter-satellite pseudo-range measurements, so called inter-satellite links (ISL). Several studies have shown the qualitative interest of ISL but do not allow to efficiently measure the quantitative impact of this new technology on space-time positioning. In this thesis, we present a differential study between a standard system (with standard satellite-to-ground links only) and system augmented by ISL. The two systems are compared under the same hypothesis and simulated within the same software. The software is made of two distinct and independent parts : the simulation which generates the noisy pseudo-ranges, and an analysis which uses a non linear adjustment procedure in order to recover the initial parameters of the simulation and compute the quantitative error budgets. For a given application, the quantitative comparison between the error budgets of both systems allow us to highlight the relative merits of the two configurations. Our results are a further step in the characterization of the interest of ISL and should prove useful for the design of future satellite navigation system design.

In the thesis, we set out to study a certain class of algebraically special spacetimes in arbitrary dimension. These are the so-called spacetimes of Weyl and traceless Ricci type N. Our work can be divided into two parts. In the first part, we study general geometrical properties of spacetimes under consideration. In particular, we are interested in various properties of aligned null directions - certain significant null directions associated with algebraic structure of the Weyl and the Ricci tensor. Since the obtained results are of geometric nature, they are theory-independent and thus hold in Einstein's gravity as well as in its various generalizations. In the second part of our work, we apply these general results in the Einstein-Maxwell p-form theory, within which spacetimes of traceless Ricci type N emerge naturally as a part of a solution of the Einstein-Maxwell equations with a null Maxwell field. Powered by TCPDF (www.tcpdf.org)

L'objet de cette thèse est l'étude mathématique de familles d'espaces-temps satisfaisant aux équations d'Einstein de la Relativité Générale. Deux approches sont considérées pour cette étude. La première partie, composée des trois premiers chapitres, examine les propriétés géométriques des espaces-temps d'Emparan-Reall et dePomeransky-Senkov, de dimension 5. Nous montrons qu'ils contiennent un trou noir, dont l'horizon des événements est à sections compactes non-homéomorphes à la sphère. Nous en construisons une extension analytique et prouvons que cette extension est maximale et unique dans une certaine classe d'extensions pour les espaces-temps d'Emparan-Reall. Nous établissons ensuite le diagramme de Carter-Penrose de ces extensions, puis analysons la structure de l'ergosurface des espaces-temps de Pomeransky-Senkov. La deuxième partie est consacrée à l'étude de données initiales, solutions des équations des contraintes, induites par les équations d'Einstein. Nous effectuons un recollement d'une classe de données initiales avec des données initiales d'espaces-temps de Kerr-Kottler-deSitter, en utilisant la méthode de Corvino. Nous construisons, d'autre part, des métriques asymptotiquement hyperboliques en dimension 3, satisfaisant les hypothèses du théorème de masse positive à l'exception de la complétude, et ayant un vecteur moment-énergie de genre causal arbitraire. / The aim of this thesis is the mathematical study of families of spacetimes satisfying the Einstein's equations of General Relativity. Two methodsare used in this context.The first part, consisting of the first three chapters of this work,investigates the geometric properties of the Emparan-Reall andPomeransky-Senkov families of 5-dimensional spacetimes. We show that they contain a black-hole region, whose event horizon has non-spherical compact cross sections. We construct an analytic extension, and show its maximality and its uniqueness within a natural class in the Emparan-Reallcase. We further establish the Carter-Penrose diagram for these extensions, and analyse the structure of the ergosurface of the Pomeransky-Senkovspacetimes.The second part focuses on the study of initial data, solutions of theconstraint equations induced by the Einstein's equations. We perform agluing construction between a given family of inital data sets andinitial data of Kerr-Kottler-de Sitter spacetimes, using Corvino'smethod.On the other hand, we construct 3-dimensional asymptotically hyperbolicmetrics which satisfy all the assumptions of the positive mass theorem but the completeness, and which display an energy-momentum vector of arbitry causal type.

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.

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 "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 "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

Submitted by Haroudo Xavier Filho (haroudo.xavierfo@ufpe.br) on 2016-04-08T18:59:56Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_PatriciaTenório_BC.pdf: 884166 bytes, checksum: 0a78095c224981af6d91420fd610f878 (MD5) / Made available in DSpace on 2016-04-08T18:59:56Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_PatriciaTenório_BC.pdf: 884166 bytes, checksum: 0a78095c224981af6d91420fd610f878 (MD5) Previous issue date: 2015-09-17 / Dissertação resultado da pesquisa de Mestrado em Letras, área de concentração Teoria da Literatura, linha de pesquisa Intersemiose, no Programa de Pós-Graduação em Letras da Universidade Federal de Pernambuco, tendo como objetivo relacionar o romance O retrato de Dorian Gray, de Oscar Wilde, com três pilares teóricos: o índice fotográfico de Charles Sanders Peirce, o tempo de Agostinho de Hipona e a prefiguração no conceito de figura de Erich Auerbach. A cada capítulo, outros teóricos são convidados a dialogar, tais como John R. Searle, Susan Sontag, Philippe Dubois, Roland Barthes, Albert Einstein, Henri Bergson, Georges Didi-Huberman e Gaston Bachelard. / Dissertation result of Master’s research in Literature, area of concentration Literary Theory, line of research Intersemiosis, in the Postgraduate Program in Literature from the Federal University of Pernambuco, having as objective order to relate the novel The Picture of Dorian Gray, by Oscar Wilde, with three theoretical pillars: the photographic index of Charles Sanders Peirce, the time of Augustine from Hippona and the foreshadowing in the concept of figure from Erich Auerbach. Each chapter, other theorists are invited to dialogue, such as John R. Searle, Susan Sontag, Philippe Dubois, Roland Barthes, Albert Einstein, Henri Bergson, Georges Didi-Huberman and Gaston Bachelard.

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