Orientadores: Ricardo Antonio Mosna, Márcio José Menon / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T03:12:41Z (GMT). No. of bitstreams: 1 QuispeAruquipa_David_M.pdf: 2372918 bytes, checksum: bb030f9f8aecc210d608f2f9005a7a49 (MD5) Previous issue date: 2017 / Resumo: Os modelos análogos são uma ferramenta muito útil quando se quer entender ou testar fenômenos em um sistema físico em termos e conceitos de outro, esses sistemas podem ser mais familiares ou mais facilmente reproduzíveis por experimentos. Este trabalho explora esta questão no contexto de modelos análogos à gravitação baseados na mecânica dos fluidos. Particularmente, estamos interessados em fornecer um modelo análogo para um fluxo radial com uma fonte/sorvedouro na origem. Começamos por considerar o caso em que a velocidade do fluxo (radial) é constante. O modelo análogo resultante é então o espaço-tempo Anti-de Sitter (ou AdS) que é conhecido por ser não-globalmente hiperbólico. Como resultado, a dinâmica dos campos neste contexto não está bem definida até que sejam estabelecidas condições adicionais na fronteira no infinito espacial do espaço-tempo AdS. A contrapartida destas condições de fronteira extra na mecânica dos fluidos proporciona uma descrição efetiva da fonte/sorvedouro que está na origem. Depois disso, nós consideramos regularizações para o modelo análogo perto da fonte/sorvedouro na origem. Logo, impomos condições sobre eles, a fim de que a dinâmica seja bem definida de modo que não são mais necessárias as condições na fronteira. Calculamos como as quantidades físicas, como a diferença de fase entre as ondas que entram e saem, são afetadas pelas regularizações. Estes resultados são então comparados com o caso AdS para compreender as principais implicações do processo de regularização, que tem o efeito de deformar a região perto do infinito espacial do AdS. Mostramos também que, sob certas condições, a diferença de fase obtida para esses espaços deformados do AdS coincide com a obtida no caso do espaço-tempo AdS / Abstract: Analogue models are a useful tool when one wants to understand or probe phenomena in one physical system in terms of concepts from another, which may be more familiar or more easily accessed by experiments. This work explores this framework in the context of analogue models of gravity based on fluid dynamics. Particularly, we are interested in providing an analogue model for a radial fluid flow with a point source/sink at the origin. We start by considering the case where the (radial) flow velocity is constant. The resulting analogue model is then the Anti-de Sitter spacetime (AdS) which is known to be non-globally hyperbolic. As a result, the dynamics of fields in this background is not well defined until extra boundary conditions at its spatial boundary are prescribed. The fluid dynamics counterpart of these extra boundary conditions provide an effective description of the point source/sink at the origin. After that, we consider regularizations of this model near the source/sink at the origin. We then impose conditions on them in order that the dynamics is well defined so that no extra boundary conditions are required. We calculate how physical quantities, like the phase difference between ingoing and outgoing scattered waves are affected by the regularizations. These results are then compared with the AdS case to understand the main implications of the regularization, which has the effect of deforming the AdS space near its spatial infinity. We also show that, under certain conditions, the phase difference obtained for these deformed AdS spaces agrees with that obtained in the AdS case / Mestrado / Física / Mestre em Física / 1490213/2015 / CAPES

Dans cette thèse, notre étude porte sur les défauts topologiques en cosmologie et en physique de la matière condensée. Nous proposons d’étudier l’analogie entre les défauts qui apparaissent dans ces domaines. Par exemple, nous discutons l’analogie entre les cordes cosmiques et les disinclinaisons présentes dans les cristaux liquides. Cependant, nous concentrons nos efforts sur l’étude de la gravité et des aspects géométriques des défauts linéaires; cordes cosmiques «ondulées» et les disinclinaisons hyperboliques. Le champ gravitationnel des cordes ondulées est analogue à celui des cordes régulières mais avec un potentiel newtonien non nul. Pour cette raison, outre le fait que l’espace-temps a une géométrie conique, les cordes produisent également une traction gravitationnelle sur les objets situés dans leur voisinage. Ceci a pour conséquence: l’apparition de nouveaux effets en plus de la lentille gravitationnelle. En réalité, nous constatons que les champs massiques et non-massiques sont confinés au voisinage de la corde quand nous examinons la propagation non perpendiculaire à son axe. Cette affirmation est basée sur l’analyse des trajectoires et l’application du formalisme ondulatoire. Enfin, nous proposons la conception d’un guide d’onde optique ayant l’indice de réfraction spécifique permettant de simuler l’effet des cordes ondulées en laboratoire. Bien que la disinclinaison hyperbolique soit très similaire à la disinclinaison ordinaire, le milieu résultant est un métamatériau anisotrope dans lequel le rapport entre les permittivités ordinaire et extraordinaire est négatif. En fait, notre analyse concernant la disinclinaison hyperbolique étant très proche de la précédente pour la corde ondulée, nous appliquons alors le formalisme ondulatoire avec des traitements d’optique géométrique pour comprendre la propagation de la lumière. Nous trouvons que pour un agencement spécifique du champ directeur du cristal liquide hyperbolique, la lumière est confinée et dirigée vers l’axe du métamatériau. Plus précisément, on obtient un dispositif optique qui concentre les rayons de lumière, quelles que soient les conditions d’injection / In this thesis, we study topological defects in cosmology and condensed matter physics. We propose to investigate the analogy between defects that appear in these two realms with respect to aspects of formation and gravity. For instance, we discuss the analogy between cosmic strings and disclinations existing in liquid crystals. In particular, we concentrate our efforts on the study of gravity/geometric aspects of two linear defects: wiggly cosmic string and hyperbolic disclination. The gravitational field of wiggly strings is analogous to the one of regular strings, but with a non-vanishing Newtonian potential. For that reason, besides the spacetime has conical geometry, the string also produces gravitational pullings on objects located in its vicinity. This new fact leads to new effects in addition to the already expected gravitational lensing. In fact, we find that both massive and massless fields are confined to the string when we examine non-perpendicular propagation to the string axis. This statement is based on the analysis of trajectories and by applying the wave formalism. Finally, we propose the design of an optical waveguide having the specific refractive index likely to simulate the effects of wiggly strings in the laboratory. Even though the hyperbolic disclination is very similar to the ordinary one, the resulting medium is an anisotropic metamaterial, in which the ratio between ordinary and extraordinary permittivities is negative. In fact, as our analysis concerning the hyperbolic medium is very close to the previous one for the wiggly string, we also apply the wave formalism together with geometrical optics treatment to understand how light propagates. Interestingly, we find that for one specific director field arrangement of the hyperbolic liquid crystal metamaterial, light is confined and directed to the metamaterial axis. More specifically, we come into possession of an optical device that concentrates light rays, no matter how they are injected in it

Orientadores: Alberto Vazquez Saa, Amir Ordacgi Caldeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T18:21:33Z (GMT). No. of bitstreams: 1 Richartz_Mauricio_D.pdf: 3399746 bytes, checksum: 3da68926653d0bbb338f76240696b246 (MD5) Previous issue date: 2011 / Resumo: A Conjectura da Censura Cosmica, proposta por Roger Penrose em 1969, afirma que singularidades resultantes de um colapso gravitacional estão sempre envolvidas pelo horizonte de eventos de um buraco negro. O objetivo desse trabalho é investigar processos de tunelamento quântico que visam violar essa conjectura. Através do formalismo de Newman-Penrose, é feita, inicialmente, uma análise de perturbações escalares, de neutrinos, eletromagneticas e gravitacionais nas métricas de Kerr e de Reissner-Nordstr om. Processos de espalhamento ondulatorio nessas métricas são estudados e coeficientes de transmissão e reflexão para ondas incidentes são calculados nos limites de baixas energias. A partir desses resultados, experimentos imaginários com o intuito de destruir o horizonte de eventos de um buraco negro e expor sua singularidade para um observador externo são propostos e analisados. A superradiância, fenômeno no qual ondas incidentes são amplificadas ao serem refletidas por um potencial espalhador, se manifesta nesses experimentos e, por isso, é tratada com detalhes e de uma forma bastante geral nesse trabalho. Por fim, experimentos que visam detectar a radiação Hawking e o fenômeno da superradiância em modelos análogos de gravitação são analisados. Em particular, um experimento proposto por mim, em colaboração com Silke Weinfurtner, cujo objetivo e investigar a possibilidade de obtenção de superradiância em laboratório, é discutido / Abstract: The Cosmic Censorship Conjecture, proposed by Roger Penrose in 1969, asserts that singularities arising from the gravitational collapse of a body are always encompassed by the event horizon of a black hole. The main purpose of this work is to investigate quantum tunneling processes whose objetive is to violate this conjecture. Using the Newman-Penrose formalism, scalar, neutrino, electromagnetic and gravitational perturbations in both Kerr and Reissner-Nordstr om metrics are analysed. Wave scattering processes in these metrics are studied and transmission and reflection coecients for incident waves are calculated in the limit of small energies. From these results, gedanken experiments with the purpose of destroying the event horizon of a black hole and exposing its inner singularity to an external observer are proposed and analysed. Superradiance, phenomenum in which incident waves are amplified when reflected by a scattering potential, manifests itself in these thought experiments and, therefore, is also treated in detail in this work. Finally, some experiments with the purpose of detecting Hawking radiation and superradiance in analogue models of gravity are analysed. In particular, an experiment proposed by me, in collaboration with Silke Weinfurtner, whose aim is to investigate the possibility of superradiance detection in laboratory, is discussed / Doutorado / Física das Particulas Elementares e Campos / Doutor em Ciências