No description available.

This thesis is devoted to studying two important aspects of braneworld physics: their cosmology and their holography. We examine the Einstein equations induced on a general (n - 2)-brane of arbitrary tension, embedded in some n-dimensional bulk. The brane energy-momentum tensor enters these equations both linearly and quadratically. From the point of view of a homogeneous and isotropic brane we see quadratic deviations from the FRW equations of the standard cosmology. There is also a contribution from a bulk Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or Reissner-Nordstrom AdS. This contribution can be understood holographically. For the AdS-Schwarzschild case, we show that the geometry on a brane near the AdS boundary is just that of a radiation dominated FRW universe. The radiation comes from a field theory that is dual to the AdS bulk. We also develop a new approach which allows us to consider branes that are not near the AdS boundary. This time the dual field theory contributes quadratic energy density/pressure terms to the FRW equations. Remarkably, these take exactly the same form as for additional matter placed on the brane by hand, with no bulk Weyl tensor. We also derive the general equations of motion for a braneworld containing a domain wall. For the critical brane, the induced geometry is identical to that of a vacuum domain wall in (n-l)-dimensional Einstein gravity. We develop the tools to construct a nested Randall-Sundrum scenario whereby we have a "critical" domain wall living on an anti-de Sitter brane. We also show how to construct instantons on the brane, and calculate the probability of false vacuum decay.

Dans cette thèse, nous étudions les équations d’Einstein dans le vide avec un champ de Killing de translation. En présence de cette symétrie, les équations d’Einstein dans le vide en dimension 3+1 peuvent s’écrire, dans le cas polarisé, comme un système d’équations d’Einstein couplées à un champ scalaire en dimension 2+1. Dans la première partie de cette thèse, nous étudions les équations de contraintes dans le cas asymptotiquement plat. Les équations de contraintes sont des équations de compatibilité qui doivent être satisfaites par les données initiales. Nous montrons l’existence de solutions pour des données assez petites, et introduisons un développement asymptotique faisant intervenir des quantités correspondant aux charges globales. Dans une deuxième partie nous montrons la stabilité de l’espace-temps de Minkowski avec un champ de Killing de translation, en temps exponentiellement grand par rapport à la petitesse de la donnée initiale. Nous travaillons dans les coordonnées d’onde généralisées. Nous introduisons une famille de métriques Ricci plates, et imposons le comportement asymptotique de nos solutions à l’extérieur du cône de lumière en choisissant un élément de cette famille de manière adéquate. Ce choix permet la convergence de nos solutions à l’intérieur du cône de lumière vers la solution de Minkowski. Dans la dernière partie de cette thèse nous étudions les équations de contraintes dans le cas compact hyperbolique. Nous montrons l’existence d’une équation limite associée aux équations de contraintes. / This thesis aim sat studying vacuum Einstein equations with a space-like Killing vector field. With this symmetry, 3+1 vacuum Einstein equations reduce, in the polarized case, to Einstein equations coupled to a scalar field in 2+ 1 dimensions. In the first part of this thesis, we study the constraint equations in the asymptotically flat case. The constraint equations correspond to computability conditions that the initial data must satisfy. We show the existence of solutions for small data, and we introduce an asymptotic expansion involving quantities which are the 2 dimensional equivalents for the global charges. In the second part, we show the stability of Minkowski space-time with a translation space-like Killing vector field in exponential time with respect to the smallness of initial data. We introduce a family of Ricci flat metrics, and we impose the asymptotic behaviour of our solutions in the exterior of the light cone by picking the right element in the family. This choice allows for the convergence to Minkowski solution in the interior of the light cone. In the last part of this thesis, we study the constraint equations in the compact hyperbolic case. We show the existence of a limit equation associated to the constraint equations.

No description available.

An analysis of the Einstein Field Equations within a Robertson-Walker Cosmology. More specifically, what values of the cosmological constant will result in a Big Bang.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-18T18:35:27Z No. of bitstreams: 1 LUIZ CORDEIRO DE LIMA NETO – DISSERTAÇÃO (PPGFísica) 2013.pdf: 963611 bytes, checksum: 83952da12a3c82dcd16e85616b111271 (MD5) / Made available in DSpace on 2018-10-18T18:35:27Z (GMT). No. of bitstreams: 1 LUIZ CORDEIRO DE LIMA NETO – DISSERTAÇÃO (PPGFísica) 2013.pdf: 963611 bytes, checksum: 83952da12a3c82dcd16e85616b111271 (MD5) Previous issue date: 2013-03-26 / Capes / Este trabalho apresenta elementos complementares da formação no nível de mestrado em Física. Discutimos, principalmente, aspectos de Relatividade Geral e Teoria Quân- tica de Campos. Deforma detalhada, explanamos a obtenção das soluções de Reissner- Nordström para as equações de Einstein que mostram a dependência dos buracos negros carregados da sua massa e da sua carga. Analisamos, também, os casos onde a massa difere numericamente da carga conhecidos como casos não-extremos, e os casos onde estas grandezas são equivalentes conhecidos como extremos. Discutimos, também, as leis da mecânica dos buracos negros e a inevitável comparação com as leis usuais da Termodinâmica e, conforme foi demonstrado por Hawking, que essas semelhanças são um fenômeno físico explicado pela a mecânica quântica. Ao rever estes estudos, Unruh percebeu que um observador acelerado em um espaço plano mede radiação térmica. Os estudos apresentados nesta dissertação constituem o embasamento necessário para o trabalho em inúmeras áreas de desenvolvimento da Física na atualidade, visto que os buracos negros carregados (em dimensões extras) possuem uma ligação com a teoria das cordas, uma das teorias mais promissoras para a construção da teoria quântica da gravitação. / This work presents complementary elements of training at the master’s degree level in Physics. We discussed, mainly, aspects of General Relativity and Quantum Field Theory. In details we expounded the obtaining of Reissner-Nordström’s solutions for Einstein’s equations that show the dependence of charged black holes on their massand charge. We also the cases in which the mass differs numerically from charge, known as non- extreme cases, and cases where the sequantities are equivalent, known as extreme. We also discuss the laws of mechanics of black holes and thein evitable comparison with the usual law softhermo dynamics and still, as demonstrated by Hawking, that the se similarities are physical phenomena explained by Quantum Mechanics. By reviewing thes estudies, Unruh realized that an accelerated observerina flat space me asures thermal radiation. The studies presented in this dissertation formed the necessary principles for research in several are as of development of physics now a days, where as the charged black holes (in extradimensions) are connected with the String Theory, one of the most promising theories for construction of the Quantum Theory of Gravitation.

In this work we study inhomogeneous cosmological models. After a brief review of applications of inhomogeneous solutions to Einstein equations in cosmology, we give a short description of the most widely used inhomogeneous cosmological models. In the second chapter we study in detail geometrical prop- erties of the Szekeres spacetime and we are concerned with the interpretation of the metric functions in different types of geometries. In the last chapter we model inhomogeneity in Szekeres spacetime. We derive formula for the density contrast and investigate its behaviour. We also derive conditions for the density extremes that are necessary for avoiding the shell crossing singularity in Szekeres spacetime. 1

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T10:00:29Z (GMT). No. of bitstreams: 1 AyalaMolina_JairoAlonso_D.pdf: 1244165 bytes, checksum: 30d706ffeeaefdce6a15f3a200327b18 (MD5) Previous issue date: 2011 / Resumo: Na atualidade, o estudo de objetos como lentes gravitacionais ou buracos negros em dimensões superiores, bem como a formulação de cosmologias de Kaluza-Klein, têm recebido cada vez maior atenção. Na tentativa de compreender melhor estes e outros temas semelhantes, o estudo das soluções exatas, assim como de algoritmos para sua geração, desempenha um papel muito importante. Neste trabalho, apresentamos as equações de Einstein no vácuo para uma classe especial de espaço-tempo D-dimensional que admite D - 2 campos vetoriais de Killing, assim como sua formulação matricial. Apresentamos também a extensão de dois algoritmos apresentados no artigo do professor Patricio Letelier, On the Inverse-Scattering Method Generation of Gravitational Waves and other New Solution-Generating Algorithms, Nuovo Cimento 97 B, 1 (1987), para depois aplicá-los na obtenção de soluções não diagonais. Igualmente estudamos a aplicação do método de Belinski-Zakharov para a obtenção de soluções solitônicas multidimensionais a partir de nossa métrica, que admite representação diagonal por blocos. Finalmente, aplicamos os algoritmos de geração apresentados às métricas de Kaluza-Klein para obter novas soluções das correspondentes teorias efetivas em quatro dimensões, assim como seus tensores de energia-momento. Exemplos de possíveis interpretações destes tensores na teoria clássica de campos (ClFT) e na mecânica de fluidos, são apresentados também / Abstract: Nowadays, the study of objects such as black holes or gravitational lenses in higher dimensions, as well as the formulation of Kaluza-Klein cosmologies, have received increasing attention. In an attempt to better understand these and other similar topics, the study of exact solutions and the algorithms for their generation, plays a very important role. In the present work we present the Einstein equations in vacuum for a special class of D-dimensional space-time which admits D - 2 Killing vector fields, as well as its matrix formulation. We also present the extension of two algorithms studied in the Patricio Letelier's paper On the Inverse-Scattering Method Generation of Gravitational Waves and other New Solution-Generating Algorithms, Nuovo Cimento 97 B, 1 (1987), to later apply them in obtaining non-diagonal solutions. We also studied the method of Belinski-Zakharov to obtain multi-dimensional soliton solutions from our metric, which admits representation diagonal by blocks. Finally, we apply the presented generation algorithms to Kaluza-Klein metrics to obtain new solutions of the corresponding effective theories in four dimensions, as well as its energy-momentum tensors. Examples of possible interpretations of these tensors in classical field theory (ClFT) and fluid mechanics, are also presented / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada

This thesis is concerned with several problems in general relativity and low energy string theory that are pertinent to the time evolution of the gravitational field. We present a formulation of the Einstein field equations in terms of variational techniques borrowed from geometric analysis. These equations yield the evolution equations for the Cauchy problems of both general relativity and low energy string theory. We then proceed to investigate the evolutionary linear stability of Schwarzschild-like solutions in higher dimensional relativity called black strings. These objects are determined to be linearly unstable. This motivates a further stability analysis of the charged p-brane solutions of low energy string theory. We show that one can eliminate linear instabilities in p-branes for sufficiently large values of charge. We also consider the characteristic problem of general relativistic magnetohydrodynamics (GRMHD). We compute the eigenvalues and eigenvectors of GRMHD and establish degeneracy conditions. Finally, we consider the initial value problem for axisymmetric GRMHD. We formulate the general Einstein and MHD equations under the assumption of a stationary axisymmetric spacetime without assuming the circularity condition.

Marginally outer-trapped surfaces (MOTSs) are found for a family of space-like hypersurfaces described by the Brill-Lindquist initial data. These hypersurfaces contain a singular ring characterized by its radius, mass and charge. Due to the ring character of the singularity, these surfaces are natural candidates for MOTSs with toroidal topology. By adjusting and employing the numerical method of geodesics, we indeed localize MOTSs of both spherical and toroidal topology, and compare the results with those obtained previously by Jaramillo & Lousto.