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General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein's equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.

Orientadores: Alberto Vazquez Saa, Amir Ordacgi Caldeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-21T19:06:37Z (GMT). No. of bitstreams: 1 Santarelli_Raphael_D.pdf: 2666477 bytes, checksum: ddd17159cb8299eef7c96d47293f68ea (MD5) Previous issue date: 2012 / Resumo: O objetivo deste trabalho é testar a validade da Conjectura Fraca da Censura Cósmica em espaços-tempo com buracos negros. Essa conjectura foi proposta por Roger Penrose em 1969, e diz que singularidades resultantes de colapso gravitacional de matéria fisicamente razoável estão sempre envolvidas por um horizonte de eventos, ou seja, escondidas de um observador externo. Apesar de muitas evidências a favor dessa conjectura, ela nunca foi provada. Nossa meta é analisar se essa conjectura pode ser violada classicamente sob especificas circunstâncias. Começaremos com uma introdução ao assunto, apresentando os conceitos que nos serão úteis ao longo de nosso trabalho. Depois investigaremos os trabalhos anteriores na área, que visaram destruir o horizonte de eventos de um buraco negro, criando assim uma singularidade nua (visível), e consequentemente violando a conjectura. Por fim, apresentaremos nossos resultados, que podem ser divididos em duas partes: (i) generalização dos casos clássicos obtidos anteriormente, e demonstração, sob dadas condições, da violação da conjectura para um buraco negro de Kerr-Newman e (ii) análise da validade da conjectura para um buraco negro com cinco dimensões em um espaço-tempo assintoticamente AdS, dando assim uma contribuição para a correspondência AdS/CFT / Abstract: The aim of this work is to test the Weak Cosmic Censorship Conjecture in black holes. This conjecture was proposed by Roger Penrose in 1969, and it states that singularities arising from the gravitational collapse of physically reasonable matter are always involved by an event horizon, i.e., they are hidden from an external observer. Despite so much evidence in favor of this conjecture, it has never been proven. Our aim is to analyze if this conjecture can be violated classically under specific circumstances. We will start with an introduction to the subject, presenting the concepts that will be useful throughout the work. After that, we will investigate the previous studies in the field that tried to destroy the event horizon of a black hole, creating a naked (visible) singularity, and hence violating the conjecture. Lastly, we will present our results, which may be divided in two parts: (i) generalization of the classic cases previously obtained, and demonstration, under specific conditions, of the violation of the conjecture in a spacetime with a Kerr-Newman black hole and (ii) study of the validity of this conjecture with a five-dimensional rotating black hole in a asymptotically AdS spacetime, making a contribution to the AdS/CFT correspondence / Doutorado / Física / Doutor em Ciências

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20176号 / 理博第4261号 / 新制||理||1612(附属図書館) / 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 田中 貴浩, 教授 川合 光, 教授 向山 信治 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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.

In classical general relativity, the values of elds on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and elds, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner–Nordström or Reissner–Nordström–deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the ‘Cauchy horizon.’ It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter elds) will become singular there in a sufciently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a ‘nal singularity,’ and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar eld in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We nd that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with afne parameter, V, along a radial null geodesic transverse to the Cauchy horizon as TVV ∼ C/V 2 with C independent of the state and C 6= 0 generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufcient to convert the Cauchy horizon into a singularity through which the spacetime cannot be extended as a (weak) solution of the semiclassical Einstein equation. This behavior is expected to be quite general, although it is possible to have C = 0 in certain special cases, such as the BTZ black hole

This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>