A finalidade deste trabalho é estabelecer as conexões entre física de buracos negros e termodinâmica, atentando para eventuais semelhanças e diferenças entre ramos aparentemente bem diversos da física moderna. Tais conexões foram inicialmente buscadas e estabelecidas na década de 1970, graças ao trabalho de S. Hawking e Jacob D. Bekenstein, entre outros, e sucessivamente aprofundadas nos anos subseqüentes, notadamente na última década. O mérito maior do primeiro foi estabelecer a emissão de radiação com espectro térmico por buracos negros em geral, mesmo aqueles desprovidos de rotação e carga (buracos negros de Schwarzschild). O segundo encarregou-se de correlacionar leis termodinâmicas clássicas com processos envolvendo buracos negros. Neste trabalho, procuramos inicialmente estudar os buracos negros de Schwarzschild e Kerr-Newman no tocante às suas propriedades gerais, bem como o problema do movimento de partículas nos espaços-tempos em questão, para discutir-se brevemente o problema de extração de energia de buracos negros, como apontado por Penrose e outros. Estabelecidas as propriedades gerais, pode-se enfim derivar a Termodinâmica destes buracos, correlacionando-se entropia e área, e obter expressões para a temperatura de corpo negro dos mesmos - em perfeita consonância com a derivação de Hawking, não abordada aqui, feita através da Teoria Quântica de Campos. Com a temperatura, pode-se estudar as capacidades térmicas, reveladores de propriedades típicas de buracos negros não compartilhadas por sistemas clássicos. A reboque destas, entra a discussão sobre a estabilidade termodinâmica de buracos negros em ensembles canônicos e microcanônicos, através do método das séries lineares, de Poincaré, fechando o presente trabalho. Assim, os capítulos 1 e 2 tratam das soluções de Schwarzschild e Kerr-Newman, respectivamente, abordando-lhes as propriedades gerais e o problema do movimento de partículas, materiais ou não, nessas geometrias. O capítulo 3 estabelece as pontes entre Termodinâmica e buracos negros, sendo crucial para o restante do trabalho. No capítulo 4 estudamos temperaturas e capacidades térmicas de diversos buracos negros, e finalmente no capítulo 5 vem o problema da estabilidade termodinâmica dos buracos negros. / In the present work, we have established the connections between black-hole physics and thermodynamics, searching for similarities and differences between these two branches of physicxs, which might look quite far apart. Such links were first sought for and established during the 1970s, thanks to the pioneering work of S. Hawking and Jacob D. Bekenstein, among others, and continuously developed in the following years, notably in the last decade. Hawking's major achievement was the prediction, from arguments based on Quantum Field Theory, that black holes radiate with a thermal spectrum, even the uncharged and nonrotating ones (the Schwarzschild black holes). Bekenstein's biggest merit was to find the link between classical thermodynamical laws and processes involving black holes. In this work, we started with Schwarzschild and Kerr-Newman black holes, working out their general properties, as well as the problem of particle motion in such spacetimes, so that we could briefly discuss the issue of energy extraction from black holes, as established by Penrose and others. Once the general features of these black holes were known, it was possible to derive the black-hole thermodynamics, due to a simple relation between black-hole entropy and area. Expressions for the black-hole temperature were then easily obtained, in perfect agreement with Hawking's own derivation, not considered here. With temperatures at hand, heat capacities could be thoroughly examined, showing intrinsic properties of black holes, not shared by classical systems. The question of thermodynamic stability of black holes arose naturally from heat capacity analysis, and we have analysed black holes in both the microcanonical and canonical ensembles, in the light of Poincaré's linear series method, completing the current work. Chapters 1 and 2 deal with the Schwarzschild and Kerr-Newman solutions, respectively, deriving their general features and working out particle motion in these geometries. Chapter 3 establishes the links between black-hole physics and thermodynamics, being of crucial importance for the subsequent chapters. Chapter 4 provides an extensive study of black-hole temperatures and heat capacities, paving the way for the last chapter, Chapter 5, concerning to thermodynamic stability of black holes.

Estudos de perturbações em sistemas gravitacionais no âmbito da Relatividade Geral vêm sofrendo grandes desenvolvimentos nos últimos anos, especialmente em face da evolução dos modernos detectores de ondas gravitacionais. Abordamos neste trabalho as perturbações de diferentes cenários. Principiamos com a métrica de Vaidya, utilizada para descrever espaços-tempos esfericamente simétricos e dependentes do tempo. Nossas simulações mostraram que as freqüências dos modos quasi-normais (MQN\'s) apresentam um novo efeito inercial para variações rápidas da função de massa, retornando depois ao comportamento adiabático. Em seguida, apresentamos um modelo para a evaporação de mini buracos negros por radiação de Hawking inspirado no cenário de criação destes objetos em aceleradores de partículas, previsto pelas novas teorias com dimensões extras. Nosso modelo, baseado na métrica de Vaidya n-dimensional, tornou possível a análise de MQN\'s resultando na possibilidade de se obter os parâmetros relevantes do buraco negro, como a sua massa inicial e o número de dimensões extras, a partir de medições experimentais. Finalmente, realizamos um estudo sobre uma nova solução denominada gravastar, proposta como um modelo alternativo para o estágio final de estrelas com grande massa. Obtivemos limites para os parâmetros da solução e verificamos a sua estabilidade frente a perturbações axiais, concluindo positivamente a respeito da possibilidade de se distinguir entre buracos negros e gravastares com base no seu espectro de MQN\'s. / Perturbative studies of gravitational systems in General Relativity have gone through big developments in the last years, especially due to the evolution of the modern gravitational wave detectors. We consider in this work different perturbations in different scenarios. Firstly we consider the Vaidya metric, mainly used to describe time-dependent spherically symmetric spacetimes. Our simulations show that the frequencies of the quasinormal modes (QNM\'s) present a new inertial effect for rapidly varying mass functions, returning afterwards to the adiabatic behavior. Next we present a model for evaporating mini black holes in particle accelerators, in the context of the new gravity models with extra dimensions. With our model, based on the n-dimensional Vaidya metric, we are able to perform a QNM analysis which results in the possibility of obtaining the parameters of the black hole, such as its initial mass and the number of extra dimensions, from the experimental measurements. Finally, we present a study of a new solution, the gravastar, proposed as an alternative model for the end state of massive stars. We obtain bounds for the parameters of the solution and verify its stability against axial perturbations. Our results indicate that the gravastar\'s QNM spectrum can indeed be used to distinguish a black hole from a gravastar.

O estudo de perturbações em buracos negros tem sido um campo de pesquisa ativo nas últimas décadas, levando a importantes contribuições para o entendimento da física de corpos compactos em geral. Para o caso de geometrias esféricas assintoticamente planas quadridimensionais, existe um panorama muito bem delineadi para a dinâmica de diversos campos de interesse. A introdução de uma constante cosmológica nas equações de Eisntein muda o caráter assintótico das soluções tipo buraco negro e neste caso, muito menos é conhecido. No trabalho desenvolvido nesta tese abordamos alguns aspectos da propagação de campos em geometrias esféricas assintoticamente de Sitter e anti-de Sitter, considerando inclusive geometrias com dimensão maios que quatro. No regime quase extremo a dinâmica é mais simples. Neste caso, são obtidas expressões analíticas para os potenciais efetivos e para os modos quase-normais, caracterizando completamente a dinâmica. Em geral, entretando, somos forçados a recorrer a métodos semi-analíticos e numéricos. Empregamos estes métodos para uma análise ampla da forma de decaimento dos diversos campos. Nossos resultados esboçam um quadro geral bastante coeso em uma grande gama de situações. / The study of pertubations in Black holes hás been na active Field of research in the last decades, leading to a better understanding of the physics of compact objects in general. In the case of asymptotically flat spherical geometries with four dimensions, there is a schematic Picture regarding the dynamics of many fields of interest. The introduction of a cosmological Constant in the Einstein equations changes the asymptotic character of the Black hole solutions, and in this case much less is known. In the work developed in this thesis we treat some aspects of the fiels propagation in spherically symmetric geometries which are asymptotically de Sitter and anti-de Sitter, considering also geometries with dimension greater than four. In the near extreme regime the dynamics is simpler. In this case, we obtain analytic expressions to the effective potentials and to the quasinormal modes, completely characterizing the dynamics. In general we are forced to use semi-analytics and numerical methods.These methods are employed in na extensive analysis of the decay modes of the fields cosidered. Our results sketch a general Picture in a wide sample of situations.

The AdS/CFT correspondence is one of the most important discoveries in theoretical physics in recent years. It states that certain quantum mechanical theories can actually be described by classical gravity in one higher dimension, in a spacetime called anti-de Sitter (AdS) space. This means that to compute any measurable quantity in the quantum theory, we can instead do a computation in classical general relativity, and vice versa. What makes this duality so useful is that it relates theories with weak coupling to theories with strong coupling and thus provides a new tool for tackling strongly coupled quantum field theories, which are notoriously difficult to handle using conventional methods. Originally discovered in the context of string theory, this duality has now found a wide range of applications, from condensed matter physics to high temperature plasmas in quantum chromodynamics (QCD).During the course of my PhD I have mostly studied time dependent processes, in particular thermalization processes, in quantum field theories using the AdS/CFT correspondence. On the gravity side, this is dual to dynamical formation of black holes from the collapse of matter fields. By studying the gravitational collapse process in detail, we can then draw conclusions about the dynamical formation of a thermal state in the dual quantum field theory. Certain quantum field theories (such as QCD) enjoy a property called confinement, which in the case of QCD states that quarks can not be isolated. Using mostly numerical methods, I have studied how confinement affects thermalization in quantum field theories. We found that sometimes the system never thermalizes and field theory observables undergo interesting quasiperiodic behaviour. In another line of research, I have studied formation of black holes in three dimensions which due to the simplified nature of three-dimensional gravity can be done using analytical methods. This has led to the discovery of new solutions of three-dimensional gravity corresponding to the formation of black holes without spherical symmetry, which can provide a deeper understanding of thermalization in two-dimensional quantum field theories. In a third line of research, I have studied higher spin gravity in three dimensions, an exotic extension of three-dimensional gravity which includes fields with spin higher than two, and found a new method to construct black hole solutions carrying higher spin charge. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Cette thèse se concentre sur des aspects de dualités holographiques reliant une théorie gravitationnelle en trois dimensions à une théorie des champs sur le bord de cette espace, c'est-à-dire en dimensions deux. Dans le premier chapitre, nous passons en revue diverses méthodes, utilisées tout au long de la thèse, pour calculer des quantités conservées en théorie de jauge et plus particulièrement en gravitation. Ensuite, dans le deuxième chapitre, nous rappelons le cas d'école des espaces-temps localement anti-de Sitter (AdS) à trois dimensions et de leur théorie duale, les théories des champs conformes en deux dimensions. Les chapitres trois et quatre sont dédiés à la présentation d'espaces-temps non-AdS considérés dans cette thèse et de la dualité dans laquelle ils sont impliqués. Le premier s'intéresse aux espace-temps warped AdS, qui peuvent être vus comme une déformation d'AdS. Leur théorie des champs duale serait une théorie des champs conforme warped. Le second se concentre sur des solutions cosmologiques, localement plates, qui seraient duales à des théories des champs invariantes sous le groupe BMS$_3$ (groupe de symétrie des espaces asymptotiquement plats). Dans le chapitre cinq, nous révisons des notions de thermodynamique que nous utiliserons pour discuter des transitions de phase entre deux géométries appartenant au même espace des phases. Par exemple, entre l'espaces-temps AdS thermique et le trou noir localement AdS. La partie originale de la thèse traite d'abord des solutions maximalement symétriques dans n'importe quelle théorie invariante sous difféomorphisme. Nous prouvons que le calcul d'entropie gravitationnel est reproduit par le comptage asymptotique d'états dans la théorie duale. Ce travail est étendu au cas des espaces-temps warped. Nous montrons également que leur entropie du bulk et du bord sont en correspondance et ce pour toutes théories de gravitation. Ceci constitue une vérification non triviale des correspondances holographiques. Nous étudions aussi leurs transitions de phase. Finalement, nous posons les premières pierres d'une nouvelle correspondance holographique, impliquant une corde noire, en trouvant un ensemble de conditions au bord cohérent. Nous discutons également la thermodynamique des cordes noires. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This thesis deals with two classes of space-time symmetries: emergent symmetries in the near-horizon region of rapidly rotating Kerr black holes and residual gauge symmetries. The main aim of the thesis is to investigate consequences and effects of these symmetries on black holes and gravitational radiation. The first class of symmetries is exploited to address questions of astrophysical relevance for force-free magnetospheres, thin accretion discs, and strong magnetic fields around Kerr black holes. We investigate how the dynamics of electromagnetic and matter fields is constrained by global conformal symmetries of the near-horizon geometry. In the context of force-free electrodynamics, we find exact solutions and classify them according to the highest weight representation of the isometry group. We introduce novel criteria to distinguish physical solutions and deduce bounds on conformal weights of electromagnetic fields. For thin accretion discs, within the Novikov-Thorne model, new properties arise in the high spin regime of the Kerr black hole. We find a novel self-similar solution and we explain the critical behaviour of the observables by symmetry arguments. Afterwards, we study an exact analytic solution to the Einstein-Maxwell theory. It describes a black hole immersed in a strong magnetic field and it shares the same near-horizon geometry of extreme Kerr black holes. We compute its total conserved mass by means of the covariant phase space formalism and study its thermodynamics. The second class of symmetries is considered in order to provide a new definition of gravitational multipole moments by means of Noether charges and by adopting the covariant phase space formalism. We show that such a definition in terms of Noether charges reproduces multipole moments in General Relativity. We propose to apply it to an arbitrary generally covariant metric theory of gravity. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

According to general relativity, appropriately accelerated masses emit gravitational radiation. With the gravitational-wave detectors reaching sufficient sensitivities for detecting astrophysical gravitational-waves, a new messenger for observing the astrophysical events has become available. However, with the current number of gravitational-wave detections, there are many unanswered questions whose answers are waiting to be discovered. Analogous to the Malmquist bias in other astronomical observation techniques, gravitational-wave detections also have an observation bias. In order to infer astrophysical distribution of the properties of gravitational-wave events from detections, this bias needs to be well understood. In this collection of studies, by investigating statistical and physical properties of gravitational-wave detection, an efficient semi-analytical method for calculating the bias was found. Further, the estimated bias was used for doing the first unmodelled inference on the mass distribution of binary black holes which showed additional structures not found by modelled inferences. Vast majority of gravitational-wave detections are binary black hole mergers. One of the mysteries of binary black holes is their formation channels. There are several proposed formation scenarios none of which is strongly favored by data. One of these channels is the so-called hierarchical triple mergers which is an dynamical formation scenario expected to have in dense environments such as globular clusters. This scenario considers a bound three black hole system which gives two consecutive mergers. In this collection of studies, it was directly tested with the detections from the three observing runs of Advanced LIGO and Advanced Virgo detectors. No significant evidence for this scenario was found, individually interesting event pairs were identified for further investigation and upper limits on the occurrence of the scenario were obtained. Gravitational-wave detectors have sensitivity on the significant portion of the sky. However, the localizations of the gravitational-wave detections are not very precise. Multi-messenger follow-ups guided by gravitational-wave detections can precisely locate the astrophysical source and gather more information by probing it with different messengers. The multi-messenger searches are done with statistical methods and it is necessary to have powerful statistical methods not to miss the valuable multi-messenger events. In the final parts of this collection of studies, optimal statistical methods for multi-messenger searches were developed and joint gravitational-wave and high-energy neutrino events were searched, both in realtime and with archival data.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18065号 / 理博第3943号 / 新制||理||1568(附属図書館) / 30923 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 中村 卓史, 教授 鶴 剛, 教授 畑 浩之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18797号 / 理博第4055号 / 新制||理||1583(附属図書館) / 31748 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 上田 佳宏, 教授 太田 耕司, 教授 嶺重 慎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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