Made available in DSpace on 2015-05-14T12:14:18Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1268026 bytes, checksum: 26540918af151a01bb663415557d121e (MD5) Previous issue date: 2010-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper deals with the influence of the gravitational field produced by a rotating black hole on quantum systems. More specifically, are considered scalar quantum particles, which are described by the Klein-Gordon equation. Initially, it was shown a way by which is possible to obtain the Kerr metric, which characterize a rotating black hole. Still on the Kerr metric, it was studied some important properties of this spacetime. Was then obtained the exact solution of the Klein-Gordon equation in the Kerr spacetime, which is given in terms of the confluent Heun s functions and, in the particular case of extreme Kerr, was obtained that the solution of the Klein-Gordon equation in this spacetime is given by the doubly confluent Heun s functions. For the Klein-Gordon equation in the Kerr spacetime, it was verified that the solution is consistent with results already known in the literature for regions near the event horizon and at infinity. Moreover, due to the difficulties inherent in the Kerr metric, was considered the limit where the black hole has low rotational speed, resulting in the metric of Lense-Thirring. In this situation, using an asymptotic method and a method in series, were obtained approximate solutions that describe the behavior of scalar quantum particles in the presence of the gravitational field produced by the body. Finally, some physical effects in Kerr spacetime were considered. / Este trabalho trata sobre a influência do campo gravitacional produzido por um buraco negro com rotação sobre sistemas quânticos. Mais especificamente, são consideradas partículas quânticas escalares, que são descritas através da equação de Klein-Gordon. Inicialmente, é mostrado uma maneira através da qual é possíıvel obter a métrica de Kerr, a qual caracteriza um buraco negro com rotação. Ainda sobre a métrica de Kerr, são estudadas algumas propriedades importantes deste espaço-tempo. Em seguida, foi obtida a solução exata da equação de Klein- Gordon no espaço-tempo de Kerr, sendo esta dada em termos das funções confluentes de Heun e, no caso particular de Kerr extremo, foi obtido que a soluçã o da equação de Klein-Gordon neste espaço-tempo é dada pelas funções duplamente confluente de Heun. Para a equação de Klein-Gordon no espaço-tempo de Kerr, verificou-se que a soluçãoo obtida é compatível com resultados já conhecidos na literatura para regiões próximo ao horizonte de eventos e no infinito. Por outro lado, devido às dificuldades inerentes á métrica de Kerr, foi considerado o limite em que o buraco negro possui baixas velocidades de rotação, resultando na métrica de Lense-Thirring. Nesta situação, usando um método assintótico e um outro método em série, foram obtidas soluções aproximadas que descrevem o comportamento de partículas quânticas escalares na presença do campo gravitacional produzido por este corpo. Por fim, alguns efeitos físicos no espaço-tempo de Kerr foram considerados.

Orientadores: Patricio A. Letelier Sotomayor e Marcelo Moraes Guzzo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-13T19:55:09Z (GMT). No. of bitstreams: 1 Castro_GianMachadode_D.pdf: 3217878 bytes, checksum: 48c026fc06d4c9e5db03014506ffc609 (MD5) Previous issue date: 2009 / Resumo: Nesta tese, estudamos o problema de um anel delgado de matéria de densidade constante com um buraco negro de Kerr em seu centro. Nosso objetivo foi resolver as equações de Einstein no vácuo com simetria axial para esse sistema gravitacional. Para fazer a sobreposição não-linear do anel com o buraco negro (BN), utilizamos o método de Belinsky e Zakharov (MBZ). Este método necessita de uma solução conhecida (solução semente) para gerar uma nova solução. Tomamos a aproximação da solução do anel em multipolos como solução semente. Como resultado, obtivemos a solução de um anel com o BN central. A expansão do anel em multipolos exige o truncamento da série. Esta aproximação introduz um erro em nossa solução. Realizamos o estudo do mesmo devido ao truncamento da série. Também estudamos a estabilidade de órbitas circulares equatoriais de partículas movendo-se ao redor do sistema anel-BN quanto a perturbações epicíclicas e verticais. Analisamos essas perturbações para os modelos de gravitação relativística e newtoniana. Como resultado, encon- tramos o efeito inesperado da duplicação das órbitas circulares de flotons para alguns valores de parâmetros relacionados com o anel e o BN, bem como zonas de estabilidade na região interna do anel. / Abstract: In this thesis, we will study the problem of a thin ring of matter of constant density with a central Kerr black hole. The aim of this work is to solve the Einstein equations in the vacuum with axial symmetry for that gravitational system. To do the nonlinear superposition of the ring with the black hole (BH), we used the Belinsky and Zakharov method (BZM). This method needs a known solution (called seed solution) to generate a new one. We took the Newtonian ring potential approximated by a multipolar expansion as seed solution. As result, we obtained the solution of a ring with a central BH. The ring multipolar expansion demands the truncation of the series. This approach introduces an error in our solution. Estimations of errors due to the truncation of the multipolar expansions are performed. We also studied the stability of equatorial circular orbits of particles moving around the system ring plus BH due to epicycle and vertical perturbations. We analyzed those perturbations for relativistic and Newtonian gravitational models. As result, we found the unexpected effect of the duplication of the photons circular orbits for certain values of parameters related with the ring and BH, as well as zones of stability in the inner area of the matter ring. / Doutorado / Relatividade e Gravitação / Doutor em Ciências

Le problème des singularités en relativité générale remonte à la première solution exacte de la théorie obtenue en 1915, à savoir celle du trou noir de Schwarzschild. Qu'elles soient de coordonnée ou de courbure, ces singularités ont longtemps questionné les physiciens qui parvinrent à mieux les caractériser à la fin des années 1960. Cela conduisit aux fameux théorèmes sur les singularités, s'appliquant à la fois aux trous noirs et en cosmologie, basés sur un comportement classique du contenu en matière de l'espace-temps résumé par des conditions d'énergie. La violation de ces conditions dans les processus quantiques pourrait indiquer que les singularités doivent être vues comme des limitations de la relativité générale, pouvant ainsi disparaître dans une théorie plus générale de la gravité quantique.Dans l'attente d'une telle théorie, nous avons pour objectif dans cette thèse d'étudier les espaces-temps de trous noirs dépourvus de toute singularité ainsi que leurs conséquences observationnelles. A cette fin, nous considérons à la fois des modifications de la relativité générale et le couplage de la théorie à des contenus en matière exotiques. Dans le premier cas nous montrons qu'il est possible de retrouver des trous noirs réguliers à symétrie sphérique connus, tout d'abord en principe avec la théorie tenseur-scalaire de gravité mimétique, puis implicitement par le biais d'une déformation de la contrainte hamiltonienne en relativité générale inspirée des techniques de gravitation quantique à boucles. Dans le second cas nous restons dans le cadre de la relativité générale, et considérons des tenseurs énergie-impulsion effectifs. Ils sont en premier lieu associés à un modèle régulier à la Hayward en rotation fournissant dans un certain régime un premier exemple de trou noir en rotation exempt de toute singularité, puis à un espace-temps dynamique décrivant la formation et l'évaporation d'un trou noir sans singularité. Pour ce dernier, nous montrons que tout modèle basé sur l'effondrement gravitationnel de coquilles de genre lumière visant à décrire l'évaporation de Hawking est voué à violer les conditions sur l'énergie dans une région non compacte de l'espace-temps. Enfin, l'étude théorique de la métrique de Hayward en rotation est accompagnée de simulations numériques d'un tel objet au centre de la Voie Lactée, obtenues à l'aide du code de calcul de trajectoires de particules Gyoto en reproduisant les propriétés connues de la structure d'accrétion du trou noir présumé Sgr A*. Ces simulations permettent d'illustrer deux régimes très différents de la métrique, avec ou sans horizon, et soulignent la difficulté d'affirmer avec certitude la présence d'un horizon à partir d'images en champ fort telles que celles obtenues par l'instrument Event Horizon Telescope. / The issue of singularities in General Relativity dates back to the very first solution to the equations of the theory, namely Schwarzschild's 1915 black hole. Whether they be of coordinate or curvature nature, these singularities have long puzzled physicists, who managed to better characterize them in the late 60's. This led to the famous singularity theorems applying both to cosmology and black holes, and which assume a classical behaviour of the matter content of spacetime summarized in the so-called energy conditions. The violation of these conditions by quantum phenomena supports the idea that singularities are to be seen as a limitation of General Relativity, and would be cured in a more general theory of quantum gravity. In this thesis, pending for such a theory, we aim at investigating black hole spacetimes deprived of any singularity as well as their observational consequences. To that purpose, we consider both modifications of General Relativity and the coupling of Einstein's theory to exotic matter contents. In the first case, we show that one can recover the static spherically symmetric non-singular black holes of Bardeen and Hayward in principle in mimetic gravity, and implicitly by a deformation of General Relativity's hamiltonian constraint in an approach based on loop quantum gravity techniques. In the second case, we stay inside the framework of General Relativity and consider effective energy-momentum tensors associated with a fully regular rotating Hayward metric and with a dynamical spacetime describing the formation and evaporation of a non-singular black hole. For the latter, we show that all models based on the collapse of ingoing null shells and willing to describe Hawking’s evaporation are doomed to violate the energy conditions in a non-compact region of spacetime. Lastly, the theoretical study of the rotating Hayward metric comes with numerical simulations of such an object at the center of the Milky Way, using the ray-tracing code Gyoto and mimicking the known properties of the accretion structure of Sgr A*. These simulations allow exhibiting the two very different regimes of the metric, with or without horizon, and emphasize the difficulty of asserting the presence of a horizon from strong-field images as the ones provided by the Event Horizon Telescope.