As propriedades termodinâmicas relacionadas a um gás composto por partículas bosônicas em geometrias esfericamente simétricas são apresentadas ao longo deste trabalho. Utilizando o formalismo proposto por Ishibashi e Kodama, verificou-se que as equações de movimento associadas aos campos escalar e eletromagnético podem ser reduzidas a uma equação tipo Schrödinger. Ao considerarmos algumas soluções esfericamente simétricas observou-se que o espectro de energia associado às partículas é discretizado. Em particular, no estudo das lightspheres, superfícies onde os fótons estão confinados em órbitas fechadas, propomos um mecanismo de quantização para as partículas bosônicas. Estudamos algumas propriedades termodinâmicas e dentro deste tratamento, é apresentada uma expressão para a densidade de energia espectral da radiação emitida. Nossos resultados sugerem que as lightspheres quando termalizadas com o seu ambiente, possuem propriedades termodinâmicas não-usuais. Ao levarmos em consideração a presença da constante cosmológica negativa, constatou-se que além de um espectro de energia discretizado, a geometria adS possui um comportamento confinante, podendo ser interpretada como uma caixa de tamanho conhecido. Considerando um gás de partículas bosônicas confinadas na geometria anti-de Sitter, obtivemos as grandezas termodinâmicas associadas tais como energia interna, entropia e pressão. Para a energia interna observamos um comportamento diferente do usual para o limite de baixas temperaturas. / The thermodynamic properties related to a gas composed of bosonic particles in spherically symmetrical geometries are presented in this work. Using the formalism proposed by Ishibashi and Kodama, we have seen that the equations of motion associated to the scalar and electromagnetic fields can be reduced to a Schrödinger-like equation. For some spherically symmetrical solutions it has been demonstrated that the energy spectrum associated with the particles is discretized. In particular, when we considered lightspheres, surfaces where photons are confined in closed orbits, we propose a quantization procedure for the bosonics particles. In this treatment, it is presented an expression for the spectral energy density of the emmited radiation. Our results suggest that lightspheres thermalized with its environment, have unusual thermodynamical properties. When taken into account the presence of the negative cosmological constant, it has been shown that, besides a discretized energy spectrum, the geometry has a confining behavior and can be interpreted as a finite size box. Considering a gas of bosonic particles confined in the anti-Sitter geometry, we obtained the associated thermodynamics quantities such as internal energy, entropy and pressure. For the internal energy, in the low temperatures limit, we observe a different behavior from the usual one.

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-10T14:48:16Z (GMT). No. of bitstreams: 1 DiazPolanco_JoseLuisBernardo_D.pdf: 1702870 bytes, checksum: b78c0c03a9b2631b73aa3127ce3e7c0b (MD5) Previous issue date: 2008 / Resumo: Apresentamos duas soluções analíticas das equações de Einstein: A primeira para o caso estático no qual um fluido carregado está em torno de um corpo massivo com propriedades magnétic~ do tipo dipolar. Esta solução se reduz à solução de Gutsunaev-Manko [Ts.I. Gutsunaev , V .8. Manko Phys. Lett. 5, 215, 19851 se o fluido carregado desaparece. Encontramos que o balanço entre os campos acoplados é devido à existência de fluxos de energia (térmica e eletromagnética) auto-compensados. A pressão de radiação compensa os efeitos dinâmicos do fluido ao redor do corpo central. Estudamos os fluxos de energia no sistema e suas propriedades termodinâmicas. Encontramos o estado termodinâmico do sistema. Esta solução contém a solução de 8chwarzschild como caso particular . A segunda solução descreve um dipolo magnético massivo e irradiante. Esta solução é dependente do tempo e descrevemos cada uma das grandezas que participam na solução. Analisamos os fluxos de energia do sistema e notamos que a radiação do dipolo diminui com o tempo chegando num estágio final do tipo dipolo magnético massivo no vácuo. Torna-se interessante pensar na possibilidade de observação destes fluxos de energia na vizinhança de objetos estrelares compactos com propriedades magnéticas extremas / Abstract: We derive analytical solutions of the Einsteinfs equations for two different cases: The first one, a static case, in which a charged fluid is around a mass with extreme magnetic properties of the dipole type. This solution reduces to the Gutsunaev-Manko solution [Ts.I. Gutsunaev , V .S. Manko Phys. Lett. 5, 215, 19851 in the abscense of the charged fluid. We found that the gravitational equilibrium of the system is achieved when the energy fluxs ( thermal and electromagnetic) are balanced and the effective radiation pressure compensates the gravitational effects in the fluid. We study the flows of energy in the system and their thermodynamics properties, we found an analytical expression for the thermodynamic state of the coupled systems. This solution contains the Schwarzschild solution as a particular case. The second solution describes a massive magnetic dipole emiting radiation decreasing in time. In this case we also found the thermodynamic state of the system. As a conclusion, we believe that our theoretical model can be applied to compact stellar systems with extreme magnetic properties / Doutorado / Relatividade e Gravitação / Doutor em Ciências

Orientador: Prof. Dr. Vilson Tonin Zanchin / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017. / No presente trabalho estudam-se buracos negros regulares e outros objetos compactos eletricamente carregados no contexto das teorias de Einstein-Maxwell. O objetivo principal do trabalho é a construção de soluções de buracos negros regulares e o estudo da estabilidade de cada solução. Com tal propósito, primeiro revisamos alguns conceitos fundamentais da Relatividade Geral e apresentamos as equações principais a serem usadas. Em particular, escrevemos explicitamente as equações de campo de Einstein para o caso de um uido anisotrópico eletricamente carregado, cuja distribuição de matéria-energia tem simetria esférica e uma equação de estado do tipo de Sitter, onde a pressão radial é igual ao negativo da densidade de energia. Em seguida, a equação de campo de Einstein é usada para busca de duas soluções, uma solução interior para a região com matéria, a qual não apresente singularidade, e outra solução exterior para a região fora da matéria que corresponde à métrica de Reissner-Nordström. Para construir uma solução à equação de campo de Einstein que seja válida em todos os pontos do espaço, aplicamos o formalismo de junção de Darmois-Israel com uma thin shell tipo-tempo. Supõe-se que a thin shell pode ter massa (densidade de energia) e pressão, na forma de um uido perfeito que obedece uma equação de estado barotrópica P = !. Uma equação de movimento para a shell é derivada das condições de junção. Encontram-se soluções estacionárias de buracos negros regulares e outros objetos compactos eletricamente carregados para escolhas especicas do parâmetro !, e encontram-se as regiões de estabilidade da solução para os casos em que a massa própria da shell é não negativa. / In the present work we study black holes and other electrically charged compact objects in the context of the Einstein-Maxwell theory. The main objective is the construction of solutions of black holes and the study of their stability. With this purpose, we rst reviewed some fundamental concepts of General Relativity introducing the main equations to be used. In particular, we write explicitly the Einstein's eld equations for the case of an electrically charged anisotropic uid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure is equal to the negative of energy density. Then, the Einstein eld equation is used to search for two solutions, an interior solution for the region with matter, which presents no singularity, and an external solution for the region outside the matter, that corresponds to the Reissner-Nordström metric. To construct a complete solution we apply the Darmois-Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the thin shell may have mass (energy density) and pressure, in the form of a perfect uid obeying the barotropic equation of state P = !. The equations of motion for the shell is derived from the junction conditions. We show that there are stationary electrically charged regular black holes solutions and other compact objects for specic choices of the ! parameter. We also show the stability and instability regions of the solutions considering the regions fo the parameter space for which the the mass of the shell is non-negative.

Orientador: Ricardo Antonio Mosna / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T04:10:22Z (GMT). No. of bitstreams: 1 Nascimento_DaniloBorimdo_M.pdf: 2195612 bytes, checksum: 9db76fa3dc3fca1c9128da411fe240b5 (MD5) Previous issue date: 2010 / Resumo: No espaço euclidiano, deformações de corpos quase-rígidos podem gerar rotações globais líquidas que obedecem, em cada instante, a lei de conservação do momento angular (o problema do gato caindo é um exemplo). Em espaços curvos, um ciclo de deformações de um corpo pode gerar não só rotações, mas também translações globais. Este fenômeno é conhecido como efeito swimming, ou natação. Avron e Kenneth apresentaram recentemente um modelo físico para descrever este fenômeno [Avron JE, Kenneth O, New J. Phys. 8, 68 (2006)]. Os autores tratam de corpos compostos por um conjunto de massas puntiformes em variedades estáticas (no contexto não-relativístico) e calculam o deslocamento obtido por um ciclo de deformações infinitesimais. Tal deslocamento é então relacionado, no caso de corpos pequenos, à curvatura do espaço ambiente. Nesta dissertação, propomos uma nova formulação para o efeito swimming utilizando formalismo de fibrados e conexões. O espaço de configurações do sistema é descrito como o espaço total de um fibrado principal, cujo espaço base é dado pelo espaço dos formatos do sistema e o grupo estrutural é (essencialmente) dado pelas isometrias da variedade ambiente. Dotando o fibrado de uma conexão que carrega consigo a informação sobre as leis físicas de conservação, expressamos o ciclo de deformações como uma curva fechada no espaço base, o movimento do corpo como o levantamento horizontal desta curva e o deslocamento resultante como a holonomia da mesma. Por meio deste formalismo, sistematizamos o cálculo do deslocamento gerado por ciclos de deformações arbitrárias, além de obter, em cada instante e analiticamente, a evolução temporal do sistema em questão / Abstract: In Euclidean space, cyclic deformations of quasi-rigid bodies can lead to net global rotations even though they satisfy, at each moment, the angular momentum conservation law (the falling cat problem is an example). In curved spaces, cyclic changes in the body shape can also lead to rotations, but also to global translations. This phenomenon is known as the swimming effect. In a recent work, Avron and Kenneth developed a formalism to describe this phenomenon in the non-relativistic context [Avron JE, Kenneth O, New J. Phys. 8, 68 (2006)], which may be used to calculate the net displacement caused by an infinitesimal cycle of deformations of a given body. This displacement is then related, for small swimmers, to the curvature of the ambient space. In the present work, we propose a new formulation for the swimming effect in terms of principal bundles and connections. The configuration space of the system is described by the total space of a principal bundle, whose base space is given by the space of shapes of the body and whose structural group is (essentially) given by the isometries of the ambient manifold. A given deformation cycleof the body then corresponds to a loop in the base space. By defining a connection in this bundle which conveys the physical conservation laws of the system, the corresponding physical motion of the body is then given by the horizontal lift of this curve in the base space, while the net displacement of the body is given by the holonomy associated with this loop. As a result we obtain, in a systematical way, the displacement generated by arbitrary deformation cycles and we get, for each instant of time, the time evolution of the system analytically / Mestrado / Geometria e Topologia / Mestre em Matemática

Orientador: Prof. Dr. Vilson Tonin Zanchin / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, Santo André, 2018.

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.

[pt] O clamor pela ampla realização material dos direitos sociais no Brasil atingiu elevados níveis neste início de século XXI. Uma vez reconhecidos formalmente pela Constituição Federal de 1988 como direitos fundamentais e, por isso mesmo, conformadores do núcleo base de nosso ordenamento jurídico, os direitos sociais ultrapassaram o nível da discussão política, constituindo objeto recorrente das lides judiciais. Cada vez mais o Judiciário passou a intervir no processo de implementação desta espécie de direitos, abandonando uma postura eminentemente passiva e formal em favor da crescente intervenção na qualidade e no próprio mérito das políticas públicas envolvidas. Este último fenômeno traz diversas conseqüências aos universos fático e jurídico, algumas das quais positivas, outras negativas, sendo certo que a presente dissertação foca, com especial atenção, as desta segunda espécie. Para tanto, opta-se pela análise do direito social à saúde, buscando-se identificar os principais problemas que se podem extrair de uma judicialização que, em diversos momentos, pode ser tida como excessiva e assistemática. Por fim, pugna-se pela necessidade de estabelecimento de limites à atuação judicial que se queira legítima, os quais devem ser construídos democrática e dogmaticamente a partir de parâmetros que tomem em séria consideração a relatividade dos direitos, seus custos, o mínimo existencial, o respeito às escolhas administrativas constitucionais e a necessidade de uma adequada ponderação de interesses, sem descurar da busca da maior efetivação possível das normas constitucionais. / [en] The clamor for ample material realization of social rights in Brazil has reached high levels at the beginning of the XXI century. Once formally approved by the 1988 Federal Constitution as fundamental rights and, therefore, compliance of the fundamental core of our legal system, social rights exceeded the level of political discussion, constituting common object of lawsuits. Increasingly, the Judiciary has to intervene in the process of implementing this kind of rights, leaving an essentially passive and formal stance in favor of increasing intervention in the quality and merit of public policies involved. This phenomenon brings several consequences for legal and factual universes, some of them positive, some negative, being sure that this paper focuses, with special attention, to this second kind. For this, the option is by analysis to the social right to health, seeking to identify major problems that can be extracted from a judicialization that, at various times, can be regarded as excessive and unsystematic. Finally, advocates by the need to establish limits on judicial action that intended to be legitimate, which must be built democratically, dogmatically and based on parameters that take into serious consideration the relativity of rights, their costs, the existential minimum, the respect for constitutional administrative choices and necessity of appropriate balancing of interests, without neglecting the search of greater possible effectiveness of constitutional rules.

>Magister Scientiae - MSc / We begin by finding a system of differential equations for the background and linearly perturbed variables in the standard, ɅCDM model, using the Einstein Field Equations, and then solving these numerically. Later, we extend this to dynamical dark energy models parameterised by an equation of state, w, and a rest frame speed of sound, cs. We pay special attention to the large-scale behaviour of Δm, the gauge invariant, commoving matter density, since the approximation Δm ≃ δm, where δm is the longitudinal gauge matter density, is more commonly used, but breaks down at large scales. We show how the background is affected by w only, so measurements of perturbations are required to constrain cs. We examine how the accelerated expansion of the universe, caused by dark energy, slows down the growth rate of matter. We then show the matter power spectrum is not in itself useful for constraining dark energy models, but how redshift-space distortions can be used to extract the growth rate from the galaxy power spectrum, and hence how redshift-space power spectra can be used to constrain different dark energy models. We find that on small scales, the growth rate is more dependent on w, while on large scales, it depends more on cs.

This thesis concerns the use of observations of gravitational waves as tools for astronomy and fundamental physics. Gravitational waves are small ripples in spacetime produced by rapidly accelerating masses; their existence has been predicted for almost 100 years, but the first direct evidence of their existence came only very recently with the announcement in February 2016 of the detection by the LIGO and VIRGO collaborations. Part I of this thesis presents an introduction to gravitational wave astronomy, including a detailed discussion of a wide range of gravitational wave sources, their signal morphologies, and the experimental detectors used to observe them. Part II of this thesis concerns a particular data analysis problem which often arises when trying to infer the source properties from a gravitational wave observation. The use of an inaccurate signal model can cause significant systematic errors in the inferred source parameters. The work in this section concerns a proposed technique, called the Gaussian process marginalised likelihood, for overcoming this problem. Part III of this thesis concerns the possibility of testing if the gravitational field around an astrophysical black hole conforms to the predictions of general relativity and the cosmic censorship hypothesis. It is expected that the gravitational field should be well described by the famous Kerr solution. Two approaches for testing this hypothesis are considered; one using X-ray observations and one using gravitational waves. The results from these two approaches are compared and contrasted. Finally, the conclusions and a discussion of future prospects are presented in part IV of this thesis.

Gravitation is the dominant influence in most astrophysical interactions. Weak-field interactions have been extensively studied, but the strong-field regime remains largely unexplored. Gravitational waves (GWs) are an excellent means of accessing strong-field regions. We investigate what we can learn about both astrophysics and gravitation from strong-field tests and, in particular, GWs; we focus upon extreme-mass-ratio (EMR) systems where a small body orbits a much more massive one. EMR bursts, a particular class of GW signals, could be used to determine the properties of massive black holes (MBHs). They could be detectable with a space-borne interferometer from many nearby galaxies, as well as the Galactic centre. Bursts could provide insightful constraints on the MBHs' parameters. These could elucidate the formation history of the MBHs and, by association, their host galaxies. The Galactic centre is the most promising source. Its event rate is determined by the stellar distribution surrounding the MBH; the rate is not high, but we still expect to gain useful astronomical information from bursts. Strong-field tests may reveal deviations from general relativity (GR). We calculate modifications that could be observed assuming metric f(R)-gravity as an effective alternative theory. Gravitational radiation is modified, as are planetary precession rates. Both give a means of testing GR. However, existing laboratory measurements already place tighter constraints on f(R)-gravity, unless there exists a screening effect, such as the chameleon mechanism, which suppresses modifications on small scales. To make precision measurements of astrophysical systems or place exacting bounds on deviations from GR, we must have accurate GW templates. Transient resonances are currently not included in the prescription for generating EMR inspiral waveforms. Their effects can be estimated from asymptotic expansions of the evolving orbital parameters. The quantitative impact on parameter estimation has yet to be calculated, but it appears that it shall be necessary to incorporate resonances when creating inspiral waveforms.