Este trabalho teve por objetivo investigar alguns aspectos dinâmicos de modelos de gravidade generalizada escalares-tensoriais e f(R), que pretendem resolver de modo mais natural o problema da existência da energia escura, que seria a componente do Universo responsável por sua expansão acelerada. Num espaço-tempo de Friedmann-Lemaître-Robertson-Walker com curvatura espacial nula foi possível escrever as equações de movimento de forma a se obter um sistema dinâmico com um número menor de variáveis e cujo espaço de fase foi estudado genericamente e esboçado para alguns modelos em particular. Em seguida, as regiões dinamicamente proibidas e os pontos fixos do espaço de fase foram analisados. Para os modelos f(R), apresentamos Lagrangianas e Hamiltonianas efetivas e deduzimos uma expressão geral para o parâmetro de equação de estado w. Discutimos ainda a equivalência entre os modelos f(R) e os escalares-tensoriais. Por fim, introduzimos o Princípio de Maupertuis-Jacobi, que permite relacionar a Lagrangiana de um sistema mecânico a uma métrica numa determinada variedade Riemanniana, para determinar singularidades que podem surgir nos modelos f(R), tanto numa métrica isotrópica como numa anisotrópica do tipo mais simples (Bianchi tipo I). Encontramos, de maneira mais direta, as mesmas singularidades já conhecidas através de métodos de análise dinâmica. / This work aims the investigation of some dynamical aspects of generalized gravity models, namely scalar-tensor and f(R) models. These models intend to solve in a more natural way the problem of the existence of the dark energy, which is supposedly the component of the Universe that causes its accelerated expansion. In a null spatial curvature Friedmann-Lemaître-Robertson-Walker spacetime, it has been possible to write the equations of movement in a fashion that allowed us to obtain a dynamical system with a reduced number of variables, whose phase space has been generically studied and depicted for some particular models. In sequence, the dynamically forbidden regions and the fixed points of the phase space have been analyzed. For f(R) models, we have presented effective Lagrangians and Hamiltonians and derived a general expression for the equation of state parameter w. Furthermore, we have discussed the equivalence between f(R) and scalar-tensor models. Finally, we have introduced the Maupertuis-Jacobi Principle, which allows one to relate the Lagrangian for a mechanical system to a metric in a certain Riemannian manifold, to determine singularities which may appear in f(R) models, in an isotropic metric as well as in an anisotropic one of the simplest kind (Bianchi type I). We have found, in a more direct way, the same singularities that arise by using dynamical analysis methods.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-02-09T13:29:06Z No. of bitstreams: 1 PDF - Paulo Robson Leite de Oliveira.pdf: 3203746 bytes, checksum: eabd1a1d941a6d86ae86acff12cc1aa7 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-02-09T21:40:23Z (GMT) No. of bitstreams: 1 PDF - Paulo Robson Leite de Oliveira.pdf: 3203746 bytes, checksum: eabd1a1d941a6d86ae86acff12cc1aa7 (MD5) / Made available in DSpace on 2017-02-09T21:40:23Z (GMT). No. of bitstreams: 1 PDF - Paulo Robson Leite de Oliveira.pdf: 3203746 bytes, checksum: eabd1a1d941a6d86ae86acff12cc1aa7 (MD5) Previous issue date: 2016-12-20 / Usually the lessons of physics at basic education little interest to students, much of this lack of interest is associated with the methodologies used to work for such knowledge, which are connected to conventional manner, the traditional approach, which still permeates the current education and plans education prepared by the teacher. This work deals with the development and implementation of an educational proposal for the theme of Universal Gravitation, from classroom and virtual meetings, aims to verify to what extent the change in teaching practices can encourage the student to participate in the construction and understanding of concepts of Physics, as well as providing other educators and students interested a material that can be used as support, or consultation, produced from the studies in the construction of the teaching proposal. Therefore the following steps of research were followed: choosing the theoretical framework; search for similar work in the main journals; development and implementation of educational proposal; and analysis of the results obtained during the intervention with students. The theoretical frameworks chosen to guide this study were divided into five parts, namely: The Physics Teaching and NCPs; Construction Concepts and Learning - Social interaction Vygotsky; History of Science and Implications for Education; Use of Blogs in Education, and Universal Gravitacion. For the realization of that research was elaborated a didactic proposal that involved classroom sessions on the subject matter and activities directed to a virtual environment (study blog), where High School students at a public school in the interior of Ceará could interact at times out of the classroom, thus extending the time pedagogical. The results achieved with this research showed, in general, students were satisfied with the resources used in the classroom and virtual classes, they demonstrated a good use and that there was a handsome learning by almost all them. / Comumente as aulas de Física na educação básica despertam pouco interesse aos estudantes, muito desse desinteresse está associado às metodologias utilizadas para se trabalhar tal conhecimento, as quais estão ligadas a maneira convencional, de abordagem tradicional, que ainda permeia a educação atual e os planos de ensino preparados pelo professor. O presente trabalho trata da elaboração e aplicação de uma proposta de ensino para o tema de Gravitação Universal, a partir de aulas presenciais e encontros virtuais, tem como objetivo principal verificar até que ponto a mudança nas práticas docentes pode incentivar o estudante a participar da construção e compreensão de conceitos de Física, além de fornecer aos demais educadores e alunos interessados um material que possa ser utilizado como apoio, ou consulta, produzido a partir dos estudos realizados na contrução da proposta de ensino. Para tanto foram seguidas as seguintes etapas de pesquisas: escolha do referencial teórico; pesquisa de trabalhos semelhantes nos principais periódicos; elaboração e aplicação da proposta de ensino; e análise dos resultados obtidos durante a intervenção com os alunos. Os referenciais teóricos escolhidos para nortearem esse trabalho foram divididos em cinco partes, sendo eles: O Ensino de Física e os PCNs; Construção de Conceitos e Aprendizagem – interação social de Vygotsky; História da Ciência e Implicações no Ensino; Uso de Blogs na Educação; e Gravitação Universal. Para a realização da referida pesquisa foi elaborada uma proposta didática que envolvesse aulas presenciais sobre o assunto em questão e atividades direcionadas a um ambiente virtual (blog de estudo), onde os estudantes de Ensino Médio de uma escola pública do interior do Ceará pudessem interagir em momentos fora de sala de aula, ampliando assim o tempo pedagógico. Os resultados alcançados com a realização desta pesquisa mostraram, em geral, que os estudantes ficaram satisfeitos com os recursos utilizados nas aulas presenciais e virtuais, demonstraram um bom aproveitamento e que houve uma aprendizagem considerável por parte de quase todos os eles.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T13:06:55Z No. of bitstreams: 1 filipedeoliveirasalles.pdf: 461360 bytes, checksum: 0a9c082265ec8357b1badcccd8374bd2 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:20:11Z (GMT) No. of bitstreams: 1 filipedeoliveirasalles.pdf: 461360 bytes, checksum: 0a9c082265ec8357b1badcccd8374bd2 (MD5) / Made available in DSpace on 2017-01-31T10:20:11Z (GMT). No. of bitstreams: 1 filipedeoliveirasalles.pdf: 461360 bytes, checksum: 0a9c082265ec8357b1badcccd8374bd2 (MD5) Previous issue date: 2011-02-15 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / A necessidade de considerar efeitos quânticos e a presença de singularidades nas soluções da Relatividade Geral indicam o desejo indispensável de estudar diferentes modelos de gravitação modificada. Além disso existe uma esperança de utilizar estes modelos para melhor entendimento da aceleração do Universo. É bem conhecido que estes tipos de teorias podem ser equivalentes aos modelos métrico-escalares, com diferentes mecanismos de equivalência. O objetivo principal do nosso trabalho é sugerir uma modificação e generalização desses mecanismos conhecidos que podem ser aplicados a uma grande variedade de teorias gravitacionais. No primeiro capítulo fazemos uma revisão histórica sobre as teorias de gravitação e uma breve introdução à teoria f(R). No segundo capítulo utilizamos funções f(R) para a métrica de Friedmann-Lemaître-Robertson-Walker, calculamos as equações e tentamos encontrar soluções do tipo exponencial. Em seguida, propomos uma generalização dessa teoria, para funções f(Xi), onde Xi pode ser R, R, Gauss-Bonnet, o quadrado do tensor deWeyleetc.Porúltimoanalisamosasperspectivasfuturasdessesmodelosdegravitação modificada. No terceiro capítulo desta dissertação sugerimos uma representação escalar-tensorial equivalente para teorias f(R). Em seguida, calculamos as equações do campo gravitacional pelo método direto, utilizando a ação escalar-tensorial e variando-a em relação à métrica esfericamente simétrica. Logo em seguida encontramos as mesmas equações de campo, porém utilizando o método de transformação conforme. Por fim veremos as perspectivas de continuidade desse trabalho, ainda em fase de conclusão. / The need to consider quantum effects and the presence of singularities in the solutions of general relativity indicate the desire necessary to study different models of modified gravity. In addition there is a hope of using these models to better understand the accelerationoftheUniverse.Itiswellknownthatthesetypesoftheoriescanbeequivalent to the metric-scalar models with different mechanisms of equivalence. The main goal of ourworkistosuggestamodificationandgeneralizationoftheseknownmechanismsthat can be applied to a wide variety of gravitational theories. In the first part we use functions f(R) for the Friedmann-Lemaître-Robertson-Walker equations and calculate the many solutions of exponential type. Then, we propose a generalization of this theory for functions of type f(Xi), where Xi can be R, R, GaussBonnet, the square of the Weyl tensor and so on. Finally we analyze the future prospects of these models of modified gravity. In the second part of this thesis is a brief introduction to the f(R) theory and suggest a scalar-tensor representation equivalent to this theory. Then, we calculate the gravitational field equations by the direct method using the scalar-tensor action and varying with respect to the spherically symmetric metric. Soon after we find the same field equations, but using the method of conformal transformation. Finally we see the prospects for continuing this work, still in the process and conclusion.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-27T11:35:41Z No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T20:52:19Z (GMT) No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Made available in DSpace on 2017-08-07T20:52:19Z (GMT). No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) Previous issue date: 2011-02-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A teoria relativística da gravitação é uma ferramenta fundamental para a compreensão da cosmologia moderna. Ela descreve a dinâmica do campo gravitacional ao longo do espaço-tempo. Dentre os possíveis modelos de universo, um dos mais comuns é o descrito pela métrica de Friedmann-Lemaitre-Robertson-Walker (FLRW). Esta métrica pode ser escrita em termos do tempo conforme e descreve um universo homogêneo e isotrópico. Neste trabalho investigamos os campos de Dirac não massivos neste modelo de universo. Os resultados mostram uma compatibilidade entre as equações de Dirac e a métrica de FLRW. Os efeitos do parâmetro de Immirzi junto com os férmions podem ser descritos em termos de um fluido perfeito usual intermediário entre a poeira e radiação. / The general relativity theory is fundamental tool for understanding the modern cosmology. In this work we investigated the massless Dirac fields in the Friedamm-Lamaitre-Robertson-Walker universe. The metric is written in terms of conformal time which describes a homogeneous and isotropic universe. We show that the effects of Immirzi parameter along with the fermions can be described in terms of a usual perfect fluid intermediate between dust and radiation.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-11-05T13:59:28Z No. of bitstreams: 1 alexandremigueldasilva.pdf: 2360446 bytes, checksum: 0d6a59c2761b474c4e71c14f7d256123 (MD5) / Approved for entry into archive by Renata Lopes (renatasil82@gmail.com) on 2018-11-06T13:29:12Z (GMT) No. of bitstreams: 1 alexandremigueldasilva.pdf: 2360446 bytes, checksum: 0d6a59c2761b474c4e71c14f7d256123 (MD5) / Made available in DSpace on 2018-11-06T13:29:12Z (GMT). No. of bitstreams: 1 alexandremigueldasilva.pdf: 2360446 bytes, checksum: 0d6a59c2761b474c4e71c14f7d256123 (MD5) Previous issue date: 2018-08-17 / O presente trabalho apresenta uma proposta de ensino de astronomia descrita numa Unidade de Ensino Potencialmente Significativa (UEPS), que consiste no uso dos conhecimentos astronômicos para explicar a Gravitação Universal. Abordamos neste trabalho a importância da Astronomia na vida cotidiana do aluno, tentando demonstrar sua utilização desde a antiguidade - nas primeiras cartas celestes para as grandes navegações e na previsão de plantio e colheita na agricultura - até os dias atuais, em que seu uso ainda é fundamental na localização e para melhor compreensão do mundo real que nos cerca. Percebemos grande dificuldade na aplicação da Astronomia na grade curricular da Educação Básica atual. Nesse sentido, apresentamos uma proposta de trabalho qualitativo que trata a Astronomia como ferramenta didática envolvida dentro de uma sequência de ensino que relata a ordem cronológica dos primeiros astrônomos culminando na quebra do paradigma do sistema geocêntrico, enfatizando a necessidade de se entender as Leis de Kepler e a Lei da Gravitação Universal de Newton. Para aplicação da sequência desenvolvemos um mapa estelar (Planisfério) que foi elaborado para facilitar as aulas de observação nas escolas de Ensino Básico. O produto educacional desenvolvido visa contemplar as escolas com dificuldades para manter um laboratório didático por meio de um material de baixo custo, cujos resultados da aplicação estão expostos neste trabalho. O objetivo desse material pedagógico é incentivar o professor a levar temas mais atraentes de astronomia para a sala de aula e, com isso, despertar o interesse dos alunos pela ciência, sem a necessidade de grandes investimentos financeiros e sem alterar o conteúdo programático da disciplina. / The present work describes a teaching proposal described in a Potentially Meaningful Teaching Units (PMTUs), which consists in using astronomical knowledge to explain Universal Gravitation. We discuss in this work the importance of Astronomy in the daily life of the student, trying to demonstrate its usage since ancient times - using the first planisphere for the great navigations, and in the forecast of planting and harvesting in agriculture - until the present days, the planisphere is used for localization and a better understanding of the real world around us. We noticed the great difficulty of applying Astronomy in the curricular grade of Basic Education in the schools nowadays. Thus we bring a proposal of qualitative work that treats Astronomy as a didactic tool involved in a teaching sequence, which reports a chronological order of the first astronomers culminating in the breaking of the geocentric system paradigm, emphasizing the necessity of understanding Kepler's laws and Newton's law of universal gravitation. For the application of the sequence, we developed a stellar map (Planisphere) which was elaborated to facilitate the observation classes in the schools of Basic Education. The educational product developed aims to contemplate the schools with difficulties to maintain a didactic laboratory with the elaboration of a product of low cost, whose results of the application are exposed in this work. The objective of this teaching material is help the teacher to bring more attractive subjects for the classroom and to arouse students interest in science, without the need for large financial investments and without modifying the programmatic content of the discipline.

Orientador: Fátima Regina Rodrigues Évora / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-25T21:06:21Z (GMT). No. of bitstreams: 1 Moreira_EdsonAdriano_D.pdf: 961513 bytes, checksum: f0259749256481cc107a396e735849f9 (MD5) Previous issue date: 2014 / Resumo: Essa Tese analisa a controvérsia entre Gottfried Wilhelm Leibniz e Isaac Newton acerca do estatuto adequado à gravitação universal newtoniana. Mais precisamente, ela procura esclarecer porque Leibniz critica a teoria newtoniana, acusando-a de postular um princípio milagroso ou uma qualidade oculta escolástica no domínio da filosofia natural, enquanto Newton, por sua vez, tentará defendê-la dessas críticas, afirmando ser a gravidade uma qualidade manifesta da matéria e o princípio que a expressa uma verdadeira lei da natureza. Para tanto, serão analisadas as cartas desses autores onde essas questões são pontualmente discutidas, quais sejam a Correspondência Leibniz-Clarke [1715-1716], a Correspondência Leibniz-Newton [1692-1693], a Carta de Leibniz a Hartsoeker [1711], a Carta de Newton ao editor das "Memoirs of Literature" [1712]; ademais, serão analisadas passagens importantes das três edições dos Princípios Matemáticos de Filosofia Natural [1687, 1713 e 1726], das cinco edições da Óptica [1704, 1706, 1717, 1721 e 1730 (edição póstuma)] e de alguns outros textos talvez menos conhecidos de Newton se comparados a estes dois, mas igualmente fundamentais para um bom entendimento das suas réplicas a Leibniz, a saber, a Carta de Newton a Bentley [1692], a Carta de Newton a Cotes [1713], a resenha que Newton publica anonimamente nas Philosophical Transactions da Royal Society sob o título de "An Account of the Book Entituled Commercium Epistolicum" [1714-1715] e uma "Conclusio" projetada por Newton para fazer parte da primeira edição dos Princípios Matemáticos de Filosofia Natural, a qual ele acabou não incluindo na versão final deste texto de 1687, mas que deu origem às considerações do famoso Escólio Geral, inserido na obra partir da sua segunda edição em 1713. Todo esse trabalho deverá, ainda, levar em conta os métodos e as entidades explicativas admitidos no panorama geral da ciência nos séculos XVI e XVII / Abstract: This Thesis analyzes the controversy between Gottfried Wilhelm Leibniz and Isaac Newton regarding the adequate statute to the Newtonian universal gravitation. More precisely, it tries to elucidate why Leibniz criticizes the Newtonian theory, accusing him of postulating a miraculous principle or a scholastic occult quality in the domain of Natural Philosophy, whereas Newton advocates his theory and protects it from such reviews claiming that gravity is a manifest quality of the matter and that the principle which expresses it is a true law of nature. To conduct this work, letters and texts written by these authors discussing such issues will be analyzed: The Leibniz-Clarke Correspondence [1715-1716]; The Leibniz-Newton Correspondence [1692-1693]; The Letter from Leibniz to Hartsoeker [1711]; and The Letter from Newton to the Editor of the "Memoirs of Literature" [1712]. Besides these letters, other important texts will be studied: passages from three editions of the Mathematical Principles of Natural Philosophy [1687, 1713 and 1726]; passages from five editions of the Optics [1704, 1706, 1717, 1721 and 1730 (a posthumous edition)]; and some other Newton¿s texts perhaps not as well-known as the other two, but equally fundamental for a good understanding of the author¿s replies addressed to Leibniz: The Letter from Newton to Bentley [1692], The Letter from Newton to Cotes [1713], the review Newton published anonymously in the Philosophical Transactions of the Royal Society under the title of "An Account of the Book Entituled Commercium Epistolicum" [1714-1715] and a "Conclusio" projected by Newton to be part of the first edition of the Mathematical Principles of Natural Philosophy, which he did not include in the final version of this text from 1687, but which was the origin to the considerations presented in the famous General Scholium, appended to his work since its second edition in 1713. It should also be mentioned that this Thesis will take into consideration the methods and the explanatory entities admitted in the general panorama of science of the XVI and XVII centuries / Doutorado / Filosofia / Doutor em Filosofia

La relativité générale (RG) et le modèle standard des particules permettent de comprendre les quatre interactions fondamentales de la nature. La formulation d'une théorie quantique de la gravitation permettrait d'unifier ces deux tenants de la physique moderne. D'après les grandes théories d'unification, une telle union est possible moyennant la brisure de certaines symétries fondamentales apparaissant à la fois en RG et dans le modèle standard telle la symétrie de Lorentz. Les violations de la symétrie de Lorentz peuvent être paramétrées dans tous les domaines de la Physique par une théorie effective du champ appelée extension du modèle standard (SME). Une violation au principe d'invariance locale de Lorentz dans le secteur gravitationnel serait supposée engendrer des perturbations dans la dynamique orbitale des corps présents dans le système solaire, notamment la Lune. Ainsi, à partir des données extrêmement précises de télémétrie laser, l'orbite lunaire peut être minutieusement analysée afin de débusquer d'éventuelles anomalies dans son mouvement. Dans cette optique, ELPN (Ephéméride Lunaire Parisienne Numérique), une nouvelle éphéméride lunaire intégrée dans le cadre du formalisme SME a été développée durant la thèse. ELPN fournit les solutions au problème lunaire sous la forme de séries temporelles datées en temps dynamique barycentrique (TDB). Parmi les solutions numériquement intégrées, mentionnons la position et la vitesse du vecteur barycentrique Terre-Lune, les angles de librations lunaires, la différence entre le temps terrestre et le TDB, ainsi que l'ensemble des dérivées partielles intégrées depuis l'équation aux variations. Les prédictions de l'éphéméride ont été utilisées afin de réduire les observations lunar laser ranging (LLR). Dans le cadre de la RG, la dispersion des résidus s'est avérée en accord avec les dispersions calculées à partir des éphémérides INPOP13b et DE430. Dans le cadre du SME minimal, l'analyse des données LLR a permis de contraindre toutes violations à l'invariance locale de Lorentz. Une grande attention a été portée à l'analyse des incertitudes afin de fournir des contraintes réalistes. Ainsi, dans un premier temps, les combinaisons linéaires de coefficients SME ont été isolées puis ajustées aux observations. Puis, dans un second temps, les incertitudes réalistes ont été déterminées par une méthode de ré-échantillonnage. L'analyse des données de télémétrie laser Lune n'a pas permis de révéler de violations au principe d'invariance locale de Lorentz agissant au niveau de l'orbite lunaire. Les prédictions de la RG ont donc été validées avec des précisions absolues allant de 10-9 à 10-12. / General Relativity (GR) and the standard model of particle physics provide a comprehensive description of the four interactions of nature. A quantum gravity theory is expected to merge these two pillars of modern physics. From unification theories, such a combination would lead to a breaking of fundamental symmetry appearing in both GR and the standard model of particle physics as the Lorentz symmetry. Lorentz symmetry violations in all fields of physics can be parametrized by an effective field theory framework called the standard-model extension (SME). Local Lorentz Invariance violations in the gravitational sector should impact the orbital motion of bodies inside the solar system, such as the Moon. Thus, the accurate lunar laser ranging (LLR) data can be analyzed in order to study precisely the lunar motion to look for irregularities. For this purpose, ELPN (Ephéméride Lunaire Parisienne Numérique), a new lunar ephemeris has been integrated in the SME framework. This new numerical solution of the lunar motion provides time series dated in temps dynamique barycentrique (TDB). Among that series, we mention the barycentric position and velocity of the Earth-Moon vector, the lunar libration angles, the time scale difference between the terrestrial time and TDB and partial derivatives integrated from variational equations. ELPN predictions have been used to analyzed LLR observations. In the GR framework, the residuals standard deviations has turned out to be the same order of magnitude compare to those of INPOP13b and DE430 ephemerides. In the framework of the minimal SME, LLR data analysis provided constraints on local Lorentz invariance violations. Spetial attention was paid to analyze uncertainties to provide the most realistic constraints. Therefore, in a first place, linear combinations of SME coefficients have been derived and fitted to LLR observations. In a second time, realistic uncertainties have been determined with a resampling method. LLR data analysis did not reveal local Lorentz invariance violations arising on the lunar orbit. Therefore, GR predictions are recovered with absolute precisions of the order of 10-9 to 10-12.

Une étude analytique et numérique de vortex métastables couplés gravitationnelle- ment et formés dans un modèle abélien de Higgs modifié est menée. Les concepts de désintégration du faux vide et de solitons topologiques sont revus. Le modèle à l’étude est comparé à d’autres modèles dans lesquels sont aussi formés des vortex. Les solutions classiques correspondant au vortex sont trouvées numériquement. Leur sensibilité au couplage gravitationnel est mise en évidence. Les zones de stabilité dans l’espace des paramètres sont également définies. Un profil dit thin-wall du vortex survient dans la limite d’un grand champ magnétique dans le coeur du vortex. La désintégration du vortex, possible en raison du vrai vide à l’intérieur de celui-ci, est dans ce cas analysée analyti- quement. Dans cette limite, l’exposant lié au taux de désintégration du vortex vaut la moitié de celui associé à la désintégration du faux vide sans vortex. Ce résultat tient peu importe la force du couplage gravitationnel. Ainsi, même une faible densité de vortex pouvant induire la désintégration du faux vide accélère grandement le processus de transition de phase et détermine le temps de vie du faux vide. Quelques commentaires concernant la limite faible gravité de l’action en théorie des champs sont ajoutés pour compléter l’étude. / Metastable vortices formed in a modified abelian Higgs model with gravity are studied both analytically and numerically. Concepts of false vacuum decay and topological solitons are reviewed. The model studied is compared to other models in which vortices are also formed. Classical solutions corresponding to a vortex are found numerically. Their sensitivity to gravitational coupling is highlighted. Zones of stability in parameter space are shown. A so-called “thin-wall” limit of the vortex is obtained for high magnetic flux whithin the vortex’s core. In that case, vortex disintegration, possible because of the true vacuum present inside the vortex, can be studied analytically. In this limit, the exponent associated to vortex tunneling decay rate is half the one associated with ordinary false vacuum decay. This results holds regardless of the gravitational coupling strength. Then, even a small density of vortices accelerates importantly the phase transition from false to true vacuum and determine the false vacuum lifetime. Comments on weak gravity limit of the action in field theory are made to complete this study.

This project contains an exposition of the basics of General Relativity up to the study of Gravitational Waves. The goal is to apply this theory to understand binary systems, how they generate gravitational waves and the energy they lose in doing so. Gravitational waves have been a topic of interest in relativity ever since their theoretical prediction in 1916. Now the interest in the subject has been renewed since LIGO's announcement of the first detection of gravitational waves, proving once again the power of General Relativity. This topic is very promising because of its implications in the future of astronomy and cosmology as a new method to obtain information about our universe.

Le cinquième télescope (CT5) du réseau H.E.S.S. (High Energy Stereoscopic System) a été inauguré en 2012. H.E.S.S. est destiné à l’observation du ciel austral dans le domaine des rayons γ et CT5, dont le seuil est d’environ 30 GeV, a permis la détection du pulsar de Vela après 24 heures d’observations. Certains scénarios de gravitation quantique (QG) prédisent une violation d’invariance de Lorentz (LIV). Celle-ci se manifeste par l’ajout de termes ∝(E/EQG)n aux relations de dispersion du photon, où E est l’énergie du quanta de lumière, EQG l’énergie caractéristique des processus de QG et n l’ordre de la correction. Cette dépendance en énergie peut être testée par des mesures de temps de vol entre photons reçus de sources astrophysiques variables (noyaux actifs de galaxies), transitoires (sursauts γ) ou encore périodiques (pulsars). Cette thèse présente l’analyse des données recueillies par CT5 sur le pulsar de Vela. Une méthode de maximum de vraisemblance ayant déjà montré sa robustesse sur d’autres types de sources a été adaptée au cas du pulsar de Vela. Aucune déviation des relations de dispersion standard n’est observée, par conséquent des limites sont placées sur EQG. La plus contraignante est obtenue pour une correction linéaire superluminique aux relations de dispersion EQG > 7.0×1015 GeV. / The fifth telescope (CT5) of the H.E.S.S. array (High Energy Stereoscopic System) was inaugurated in 2012. H.E.S.S. is designed to scrutinize the southern γ ray sky and CT5, whose threshold is about 30 GeV, allowed the Vela pulsar detection in 24 hours observation time. Some quantum gravity (QG) scenarios predict a violation of Lorentz invariance (LIV). This could manifest by additional terms ∝(E/EQG)n to the photon dispersion relations, where E is the light quantum energy, EQG the typical scale at which QG processes are expected to occur and n the order of the correction. This energy dependence could be tested by time of flight measurements between photons emitted from variable (active galactic nuclei), transient (gamma ray bursts) or periodical (pulsars) astrophysical sources. This thesis presents the analysis of the CT5 collected data from the Vela pulsar. A maximum likelihood method already successfully applied to other source species has been adapted here to the Vela pulsar. No deviation from standard photon dispersion relations is observed, therefore limits have been placed on EQG. The most restrictive result has been obtained for a superluminal linear correction to the dispersion relations EQG > 7.0×1015 GeV.