This project aims to study general relativity to the extent to understand the occurrence and behaviors of closed timelike curves (CTCs) in several exact solutions of Einstein’s field equations. The rotating black hole solution, the Gödel universe and the cosmic string solutions are studied in detail to show how CTCs arise in these spacetimes. The chronology-violationing paradoxes and other unphysical aspects of CTCs are discussed. The spacetimes where CTCs arise possess properties which are argumented to be unphysical, such as lack of asymptotic flatness and being innite models. With quantum computational networks it is possible to resolve the paradoxes which CTCs evoke. With all these attempts of resolving CTCs, our conclusion is that CTCs exist quantum mechanically, but there is a mechanism which inhibits them to be detected classically. / Detta projekt åsyftar att studera allmän relativitet i den grad att kunna förstå uppkomsten och företeelsen av tidsliknande slutna kurvor (CTC) i några exakta lösningar till Einsteins ekvationer. Dessa lösningar inkluderar Gödel universen, kosmiska strängar och det roterande svarta hålet, där CTC studeras i mer detalj. CTC är kronologi-kränkande företeelser och paradoxen som uppstår presenteras, samt de argument som ligger till grund till att CTC inte är fysikaliskt verkliga objekt. De tidrum där CTC uppkommer delar gemensamma egenskaper som anses ofysikaliska, som att vara icke asymptotiskt platta tidrum, samt att vara oändliga modeller. Med kvantinformatiska nätverk kan CTC illustreras och de klassiska kronologi-paradoxen kan rättas ut. Slutsatsen är att CTC existerar kvantmekaniskt, men det fnns en mekanism i verkligheten som förhindrar dessa att bli detekterade klassiskt.

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The existence and -if exists- the nature of the solutions of the scalar wave equation in spacetimes with closed timelike curves are investigated. The general properties of the solutions on some class of spacetimes are obtained. Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results of 2+1 dimensions are verified by using numerical methods.

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T22:19:55Z (GMT). No. of bitstreams: 1 Rosa_ValeriaMattosda_D.pdf: 1232759 bytes, checksum: e4b5f9dd20a1bb1f521f2972b43bbfaf (MD5) Previous issue date: 2007 / Resumo: Várias soluções das equações de Einstein admitem curvas tipo-tempo fechadas (CTCs). Estudamos o comportamento deste tipo de curva quanto à estabilidade linear. Analisando as CTCs no universo de Gödel, encontramos que elas são linearmente estáveis, assim como as curvas desse tipo encontradas em um exemplo particular de métrica tipo-Gödel com fundo plano. As CTCs que aparecem no modelo contendo uma única corda cósmica girante também apresentam estabilidade linear. Estudamos todos os exemplos conhecidos de soluções das equações de Einstein que possuem geodésicas tipo-tempo fechadas (CTGs). Encontramos que a CTG apresentada pelos autores da solução dos dois perjeons não é linearmente estável, mas obtivemos condições, para os parâmetros desse modelo, sob as quais ela admite outras CTGs e, sob condições mais restritivas, obtivemos CTGs linearmente estáveis. As CTGs apresentadas por Soares em seu modelo topológico e por Grøn e Johannesen em seu modelo da núvem de cordas não possuem estabilidade linear. Já as CTGs de uma das soluções dada por van Stockum foram analisadas e verificamos que são linearmente estáveis. Encontramos CTGs em um exemplo particular de métrica tipo-Gödel com fundo conformemente plano, e estas também são estáveis. Analisamos, também, a deformação provocada pelo buraco negro de Schwarzschild ao ser colocado em um espaço-tempo com uma corda cósmica girante. Encontramos as CTGs desse espaço-tempo e determinamos as condições para que estas sejam estáveis / Abstract: Several solutions of Einstein¿s field equations admit closed timelike curves (CTCs). We study the linear stability of this kind of curve. We analyze the CTCs in Gödel universe and we find that these curves are stable. The same occurs with the CTCs of a particular case of Gödel-type metric with flat background and with CTCs of a model that contains a single spinning cosmic string. We study all known solutions of Einstein¿s equations that contain closed timelike geodesics (CTGs). We find that the CTG presented by Bonnor and Steadman in their model of two Perjeons is not stable under linear perturbations, but we present conditions to have stable CTGs in this model. The CTGs presented by Soares in his topological model and those presented by Grøn and Johannensen in their model of the cloud of strings are not stable. But, analizing the CTGs presented by Steadman in a solution gave by van Stockum, we conclude that these curves are stable. Besides these known CTGs, we find this kind of curve in a particular case of G¨odel-type metric with conformally flat background and we also find that they are stable. We also study the deformation that a Schwarzschild black hole causes in the spacetime of a single spinning cosmic string. We find the CTGs of this new spacetime and we determine conditions to have linear stability / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada

Les travaux récents en fondements de la théorie quantique (des champs) et en information quantique relativiste tentent de mieux comprendre les effets des contraintes de causalité imposées aux opérations physiques sur la structure des corrélations quantiques. Le premier chapitre de cette thèse est consacré à l'étude des implications conceptuelles de la non-localité quantique, notion qui englobe celle d'intrication dans un sens précis. Nous détaillons comment les récentes approches informationnelles tentent de saisir la structure des corrélations non-locales, ainsi que les questions que ces dernières soulèvent concernant la capacité d'un observateur localisé à isoler un système de son environnement. Le second chapitre détaille les effets de l'invariance de Poincaré sur la détection et la quantification de l'intrication. Cette invariance impose que tous les systèmes soient modélisés en dernière instance dans le cadre de la théorie des champs, ce qui implique qu'aucun système à énergie finie ne puisse être localisé, ainsi que la divergence de toute mesure d'intrication pour des observateurs localisés. Nous fournissons une solution à ces deux problèmes en démontrant l'équivalence générique qui existe entre une résolution spatiale finie des appareils de mesure et l'exclusion des degrés de liberté de haute énergie de la définition du système observé. Cette équivalence permet une interprétation épistémique du formalisme quantique standard décrivant les systèmes localisés non-relativistes et leurs corrélations, clarifiant ainsi l'origine des mesures finies d'intrication pour de tels systèmes. Le dernier chapitre explore un cadre théorique récemment introduit qui prédit l'existence de corrélations quantiques sans ordre causal défini. Procédant par analogie avec le cas des corrélations non-locales, nous présentons quelques principes informationnels contraignant la structure de ces corrélations dans le but de mieux en comprendre l'origine physique. / Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincaré invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.