Einstein’s equations are derived by following Jacobson’s thermodynamic method. It is seen that a family of possible field equations exist which satisfy the thermodynamic argument. Modified theories of gravity are addressed as possible candidates for replacing dark matter as an explanation for anomalous cosmological phenomena. Many of the proposed modified theories are not powerful enough to explain the currently observed phenomena and are rejected as viable theories of gravity. A surviving candidate, TeVeS, is further analyzed under the aforementioned thermodynamic argument to check for its consistency with thermodynamics.

RESUME :Cette thèse a pour objet d'analyser et d'expliquer les causes et les conséquences des politiques de diversification liées aux investissements dans le secteur bancaire français à la recherche de la taille critique. Au cours de ces dernières décennies, ces organisations ont diversifié leurs investissements par des stratégies de croissance externe et interne. Elles ont également investi dans des secteurs de l'activité économique qui n'ont pas de liens directs avec le métier principal de la banque. Les stratégies de croissance souvent porteuses ont dû faire face aux situations de crise financière majeure ces deux dernières années. L'analyse des stratégies de croissance externe, interne et de diversification ainsi que l'analyse financière des bilans des banques, aux prises avec des mutations liées aux nouvelles technologies de l'information et de la communication, démontreront la pertinence des choix des investissements entre les stratégies du « be to be » et du « be to c ». Les exigences liées aux ratios prudentiels, la théorie de la valeur, celle de l'agence, les avantages concurrentiels et la théorie de la gouvernance sont autant d'outils méthodologiques et de champs d'investigations que nous utiliserons pour analyser la pertinence des choix stratégiques de diversification pour atteindre un niveau de performance tel, qu'il puisse valider la taille optimale, dite taille critique.La recherche opérationnelle permettra d'une part d'identifier les phénomènes stratégiques et d'autre part d'élaborer un modèle de formalisation lié à la pertinence de la taille critique. De nombreuses approches identifient la taille, via des critères multiples sans en dégager une matrice globale d'exploitation. L'objet théorique de recherche s'appliquera à formaliser ce modèle.Du point de vue méthodologique nous analyserons les Banques Françaises à réseaux de 1990 aux années 2000 – 2006, dans une démarche transversale. Cette approche devrait nous permettre d'un point de vue opérationnel de trouver également des « niches » d'activité porteuse.Au niveau théorique, nous nous appuierons sur les travaux de recherche de Michael Porter « L'Avantage Concurrentiel » et spécifiquement sur les notions de « stratégies génériques ».Si aujourd'hui la notion de « chaîne de valeur » est clairement identifiée dans le secteur bancaire, il n'en demeure pas moins que les stratégies de diversification de ces entreprises transforment cette donnée et que leur rentabilité s'en trouve modifiée, grâce au degré de performance. Néanmoins, la crise que traverse le système bancaire et financier depuis début 2007 vient à la fois renforcer et contredire certaines de ces théories que nous aurons à analyser. / SUMMARY:This thesis aims to analyze and explain the causes and consequences of diversification policies related to investments in the French banking sector in the search for the critical size. Over the last decades, these organizations have diversified their investment by implementing internal and external development strategies. They have also invested in some economic sectors which are not directly linked to the main banking activity. Beneficial growth strategies have had to face major financial crisis over the last two years. By analysing external, internal and diversification development strategies, and the bank balance sheets, that are subject to changes with new information technologies and communication, the choice of investment between "be to be" strategies and "be to c 'will be relevant. The requirements attached to prudential ratios, the value theory, the agency's theory, the competitive advantages and the governance theory are all methodological tools and investigative fields that will be used to analyze the importance of the strategic choices of diversification to reach a level of performance, which can validate the optimal size, called critical size.Operational research on the one hand will allow the identification of the strategic process and on the other hand the development of a formal model linked to the importance of the critical size. Many approaches identify the size; through multiple criteria without defining a global matrix of operation... The purpose of this theoretical research will assure the formalization of this model.From the methodological point of view we will analyze the French banking networks from 1990 to the years 2000 -2006, in a transversal approach. This approach should also allow us from an operational point of view, to find "niches" of profitable activity.At the theoretical level, we will refer to Michael Porter's research of "The Competitive Advantage" and specifically on the notions of "generic strategies".If today the term “chain of value” is clearly identified in the banking sector, the diversification strategies of these companies are however modifying these data and their profitability, thanks to the performance level. Nevertheless, the crisis in the banking and financial system since early 2007 is both reinforcing and contradicting some of the theories that will be analyzed.Moreover, the neo institutional theories will allow us to show that the bankers' rationale is limited and their decisions are dependent on a number of factors, such as the issue of the transaction costs, the informational asymmetric and the contingency factors between strategy and structure. Decision choices do not depend only on opportunities but also on the conditions that make them feasible and profitable for the organization.

吀e so-called "trumpet" initial data has recently received mu挀 a琀ention as a potential candidate for the natural black hole initial data to be used in 3+1 numerical relativity simulations with 1+log foliation. In this work we first derive a variant of the maximal trumpet initial data that is made to move on the numerical grid by the means of a Lorentz boost and write a numerical code that constructs this boosted trumpet initial data. We also write a numerical code for calculating the Krets挀mann scalar from the 3+1 variables, to be used in analysing the data from our simulations. With the help of those two codes, we study the behaviour of the boosted trumpet initial data when evolved with the BSSN formulation of the Einstein equations, using 1+log slicing and the Γ-driver shi昀 condition.

On étudie dans cette thèse le système d'Einstein-Lichnerowicz, aussi appelé système des contraintes conformes. C'est un système d'équations aux dérivées partielles nonlinéaires elliptiques, obtenu après application de la méthode conforme, qui intervient en théorie de la Relativité Générale, plus précisément dans l'analyse des équations d'Einstein comme un problème d'évolution.Le résultat principal de notre thèse, démontré en toutes dimensions supérieures ou égales à 3, est un résultat de stabilité du système des contraintes conformes. Il exprime la dépendance continue de l'ensemble des solutions du système des contraintes conformes en les grandeurs physiques de la méthode conforme. En ce sens, c'est un résultat de structure sur l'ensemble des solutions du système d'Einstein-Lichnerowicz.Ce résultat exprime aussi la pertinence physique d'une construction physique naturelle qui intervient dans le cadre de la méthode conforme, que nous appelons dans le manuscrit construction de Choquet-Bruhat-Geroch-Lichnerowicz et que nous décrivons en détail.Nous obtenons aussi dans cette thèse des résultats d'existence pour le système d'Einstein-Lichnerowicz. Un premier résultat d'existence est obtenu par des méthodes non-variationnelles. Un résultat indépendant de multiplicité est obternu comme conséquence du résultat de stabilité énoncé plus haut. / We investigate in this work the Einstein-Lichnerowicz constraints system, also called conformal constraints system. It is an elliptic system of nonlinear partial differential equations obtained through the conformal method, and arising in Mathematical General Relativity in the analysis of the Einstein equations as an evolution problem.Our main result, proven in any dimension greater than 3, is a stability result for the conformal constraints system. It asserts the continuous dependence of the set of solutions of the conformal constraints system in the physical parameters of the conformal method. It is then a structure result on the set of solutions of the Einstein-Lichnerowicz constraints system.Our result can be rephrased in terms of the physical relevance of a physical construction naturally arising in the context of the conformal method, that we call Choquet-Bruhat-Geroch-Lichnerowicz formalism and that we describe in detail.We also obtain in this work existence results for the Einstein-Lichnerowicz constraints system. A first existence result is obtained via non-variational methods. An independent multiplicity result is obtained as a consequence of the aforementioned stability result.

The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was shown that the corresponding constraint violations subside after a few orbits, becoming comparable to those found in evolutions of standard conformally flat, helically symmetric binary initial data. This dissertation presents the first spinning neutron star binary simulations in circular orbits with a orbital eccentricity less then 0.01. The initial data sets corresponding to binaries with spins aligned, zero and anti-aligned with the orbital angular momentum were evolved in time. These simulations show the orbital “hang-up” effect previously seen in binary black holes. Additionally, they show orbital eccentricities that can be up to one order of magnitude smaller than those found in helically symmetric initial sets evolutions. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2013.

Neste trabalho nós propomos uma estratégia Euclidiana para entender o efeito Unruh. Com este objetivo, nós inicialmente o estudamos para campos livres escalares sem massa, numa forma que é normalmente apresentada aos físicos e que é mais próxima ao trabalho original de Unruh I321| . Logo em seguida, deduzimos o efeito de um ponto de vista algébrico. Com este objetivo, estudamos as propriedades e as definições de estados KMS para compreender como um estado de equilíbrio é descrito na abordagem algébrica. Apresentamos os axiomas de Wightman para campos escalares assim como os de Osterwalder-Schrader. Usamos, então, o Teorema de Bisognano-Wichmann para estes campos e concluímos, baseados no trabalho de Sewell [27], que um observador uniformemente acelerado vê o estado de vácuo dos observadores inerciais como um estado KMS, e portanto, como um estado de equilíbrio. Novamente, concluímos a existência do efeito Unruh. Finalmente estudamos algumas relações entre probabilidade e análise funcional. Este estudo é fundamental para o entendimento do trabalho de Klein e Landau [15] e de Gérard e Jakel [7]. Estes trabalhos afirmam que existe uma relação biunívoca entre certos estados KMS e certos processos estocásticos (Klein e Landau) e uma relação entre certos processos estocásticos e espaços de trajetórias generalizados (Gérard e Jakel). Usando estes trabalhos e as funções de Schwinger para campos escalares, deduzimos o efeito Unruh de uma nova maneira. Acreditamos que este trabalho mostra um ponto de vista interessante do efeito Unruh e ilustra o uso do formalismo Euclidiano em teorias quânticas dos campos. Mesmo que algumas demonstrações para uma prova completa do efeito, usando técnicas Euclidianas, não são obtidas, devido às dificuldades técnicas encontradas, acreditamos que o material apresentado neste trabalho fornece, no mínimo, uma boa estratégia para a compreensão completa deste fenômeno físico. Além disto, as técnicas que são mostradas podem ser usadas em diversos problemas, como a construção de campos interagentes a uma temperatura finita, que permanecem atuais e promissores. / This paper proposes a Euclidean strategy to understand the Unruh effect. On that ground we first study it for free massless scalar fields the way it is usually presented to pliysicists, which is closer to Unruh\'s original work [32]. Then we infer the effect from an algebraic perspective. We study the proprieties and definitions of KklS states in order to understand the description of an equilibrium state in the algebraic approach. We present the Wightman\'s as well as Osterwalder-Schrader\'s axioms for scalar fields. Then we use the Bisognano-Wichmann theorem for these fields and conclude, based on Sewell work 1271, that a uniformly accelerated observer will observe tlie vacuum state of inertial observers as a KMS state and thus as an equilibrium state. Once again we infer the existence of the Cnruh effect. Finally we study some relations between probability and functional analysis. This study is crucial for understanding the work of Klein and Landau 1151 as well as of Gérard and Jakel (71. They state there is a biunivocal relation between certain KMS states and certain stochastic processes (Klein and Landau) and a relation between certain stochastic processes and generalized path spaces (Gérard and Jakel). Lsing these works and Schwinger functions for scalar fields, we deduce tlie Unruh effect in a new way. LVe believe this work shows an interesting aspect of the Unruh effect and represents the use of Euclidean formalism in quantum field theory. Although some demonstrations for a complete proof of the Unruh effect using Euclidean techniques were not obtained due to technical difficulties we faced, we believe the material presented in this paper provides at least a good strategy for the complete understanding of this physical phenomenon. Furthermore the techniques shown, which remain current and promising, can be used in different problems, sudy as the construction of interacting fields at a finite temperature.

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

Cerca de 25% do conteúdo energético do universo se encontra sob uma forma de natureza ainda não determinada e é conhecida pelo nome de matéria escura. Desde as primeiras especulações acerca de sua existência (Zwicky ~ 1933), vários modelos foram propostos na tentativa de justificar os dados observacionais encontrados mas, até hoje, nenhum deles foi capaz de cumprir essa tarefa a contento. Nesta dissertação, apresentaremos uma breve discussão desses modelos, além de propor um novo, baseado na idéia de que tanto a matéria escura quanto a energia escura possam ser compostas pelo campo escalar de Born-Infeld. / Nearly twenty five percent of the energetic content of the universe appears in a form that is still unknown and is named dark matter. Since the first speculations about its existence (Zwicky ~1933), many models have been proposed trying to justify all the observed data but, until now, none of them has been able to solve this problem. In this monography, we will present a brief discussion about these models and propose a new one, based on the idea that both dark matter and dark energy could be the Born Infeld scalar field.

Obtivemos famílias de soluções estáticas e esfericamente simétricas para buracos negros numa brana com vácuo, constante cosmológica não nula e imersa num bulk 5-dimensional assintoticamente anti-de Sitter. Para o caso das geometrias assintoticamente de Sitter, o único membro da família obtida foi a geometria Schwarzschild-de Sitter extrema. Para o caso de geometrias assintoticamente anti-de Sitter, obtivemos toda uma família de soluções, onde cada elemento desta família é determinado por uma constante C. Estudamos o comportamento destas soluções próximo e longe do horizonte de eventos. A seguir, analisamos a evolução de um campo escalar não massivo no exterior dos buracos negros obtidos. Verificamos analiticamente e numericamente o comportamento do potencial efetivo em função da coordenada tartaruga próximo ao horizonte de eventos. Para qualquer geometria ou solução desta família observamos que o campo escalar não massivo decai com o tempo, e o tipo de decaimento depende do valor da constante C. Assim, toda a família de soluções obtida mostrou-se estável. / We found classes of static and spherically symmetric black hole solutions on the brane for a vacuum configuration, non-null cosmological constant, embedded into a 5-dimensional asymptotically anti-de Sitter bulk. In the asymptotically de Sitter case, the only solution obtained was the extreme Schwarzschild-de Sitter geometry. In the asymptotically anti-de Sitter case, a class of solutions was obtained where a particular geometry is fixed by a constant, C. We studied the behaviour of these solutions near and far from the horizon. Next, we studied the time evolution of a scalar field outside the black hole. For the effective potential as function of tortoise coordinate, the analytical results near the horizon agree with numerical calculations. The scalar field decays with time and the particular form of decay depends of the value for C. Thus, all solutions in the obtained class are stable.

No presente trabalho construímos o potencial nucleon-nucleon devido à troca de dois píons dentro do contexto relativístico da teoria de perturbação quiral, formulada por Becher e Leutwyler. No estudo do espalhamento píon-nucleon, eles desenvolveram um método que exibe a regra de contagem de potências, mantendo a invariância relativística. Os autores também chamam a atenção para um problema presente na formulação de bário pesado, de que sua série quiral não converge na região de baixa energia em torno de t=4µ2, onde µ é a massa do píon. Nós mostramos que este problema é bastante relevante para o potencial nucleon-nucleon, principalmente pelo fato dessa região de energia determinar suas características assintóticas. A dinâmica da troca de dois píons na interação nucleon-nucleon é determinada pelas sub-amplitudes píon-nucleon. Partindo da sub-amplitude de Becher e Leutwyler, obtemos diagramas classificados em três famílias, de acordo com sua topologia e constantes de acoplamento envolvidas. Na definição do potencial subtraímos, da amplitude relativéstica, a iteração da troca de um píon, seguindo a prescrição de Blankenbecler e Sugar. O nosso potencial até a ordem q4 é expresso em termos de seis funções básicas, associadas a integrais de loop, calculadas relativisticamente. Ele mantém as propriedades assintóticas corretas, desde que as integrais básicas não sejam expandidas. Forçando tal expansão, com o objetivo de comparar com os resultados de Entem e Machleidt, observamos concordância na maioria dos termos. Algumas diferenças estão associadas à discrepância na relação de Goldberger-Treiman, indicadas por GT, e dois termos, a contribuições de dois loops. As demais, muito provavelmente estão relacionadas à iteração da troca de um píon. No espaço de configuração, comparamos os nossos resultados com a parte de médio alcance de duas versões do potencial de Argonne, AV14 e AV18. Observamso uma boa concordância apenas para o potencial central isoescalar, o canal mais importante para a fenomenologia. Para as demais componentes, temos discrepâncias inclusive entre as versões AV14 e Av18. Com base na classificação da dinâmica em três famílias e analisando suas contribuições para cada componente, apresentamos uma proposta de como evitar ambiguidades desse tipo na construção de potenciais fenomenológicos. / This work is devoted to the construction of a two-pion Exchange nucleon-nucleon potential in the framework of the relativist chiral perturbation theory, formulated by Becher and Leutwyler. In their study of pion-nucleon scattering they developed a method to regain the Power counting rules while keeping Lorentz invariance. These authors also Drew attention to a problem present in the heavy baryon formulation, that is chiral serie does not converge in the low-energy region around t=4µ2, where µ is the pions mass. We have shown that this problem is rather relevant to nucleon-nucleon potential, mainly due to the fact that this range of energy determines its asymptotic properties. The dynamics of the two-pion Exchange nucleon-nucleon interaction is determined by pion-nucleon sub-amplitudes. Starting from Becher and Letwylers sub-amplitude, we obtain diagrams classified in three families, according to their topology and the coupling constants involved. In the definition of the potential we substract, from the relativist amplitude, the iteration o fone-pion Exchange, following the prescription of Blankenbecler and Sugar. Our potential up to order q4 is expressed in terms of six basic functions associated to relativistic loop integrals. It keeps the correct asymptotic properties, as long as we do not expand the basic integrals. Forcing such na expansio, in order to compare it with the results from Entem and Machleidt, we observe na agreement in the majority o terms. Some differrences are associated to the Goldberg-Treiman discrepancy, indicated by GT, and two terms come from two loop calculations. The remaining ones are probably related to the prescription adopted for the iteration o fone-pion exchange. In configuration space we compare our results with the médium-range component of two versions of the Argonne potential, AV14 and AV18. We obtain agreement only for the central isoscalar potential, the most important to phenomenology. Regarding other channels, we observe discrepancies even between AV14 and AV18. Based on the classification of the dynamics in three families and analysing their contributions to each component, we propose a way to overcome such ambiguities in the construction of phenomenological potentials.