Dissertations / Theses on the topic 'Lorentzian'
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Botros, Amir A. "GEODESICS IN LORENTZIAN MANIFOLDS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/275.
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We present an extension of Geodesics in Lorentzian Manifolds (Semi-Riemannian Manifolds or pseudo-Riemannian Manifolds ). A geodesic on a Riemannian manifold is, locally, a length minimizing curve. On the other hand, geodesics in Lorentzian manifolds can be viewed as a distance between ``events''. They are no longer distance minimizing (instead, some are distance maximizing) and our goal is to illustrate over what time parameter geodesics in Lorentzian manifolds are defined. If all geodesics in timelike or spacelike or lightlike are defined for infinite time, then the manifold is called ``geodesically complete'', or simply, ``complete''. It is easy to show that the magnitude of a geodesic is constant, so one can characterize geodesics in terms of their causal character: if this magnitude is negative, the geodesic is called timelike. If this magnitude is positive, then it is spacelike. If this magnitude is 0, then it is called lightlike or null. Geodesic completeness can be considered by only considering one causal character to produce the notions of spacelike complete, timelike complete, and null or lightlike complete. We illustrate that some of the notions are inequivalent.
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León, Guzmán María Amelia. "Clasificación de toros llanos lorentzianos en espacios tridimensionales." Doctoral thesis, Universidad de Murcia, 2012. http://hdl.handle.net/10803/83824.
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Un problema clásico en geometría lorentziana es la descripción de las inmersiones isométricas entre los espacios lorentzianos de curvatura constante. En este trabajo nos centramos en la clasificación de las inmersiones isométricas del plano lorentziano en el espacio anti-de Sitter tridimensional. Damos una fórmula de representación de estas inmersiones en términos de pares de curvas (con posibles singularidades) en el plano hiperbólico. Esto nos permite resolver los problemas propuestos por Dajczer y Nomizu en 1981.
De entre todas las inmersiones isométricas del plano lorentziano en el espacio anti-de Sitter, algunas de ellas corresponden a toros lorentzianos (los ejemplos más sencillos son los toros de Hopf). Como aplicación de nuestra anterior descripción, probamos que todos estos toros pueden obtenerse a partir de dos curvas cerradas en el espacio hiperbólico.
Finalmente, demostramos que los toros de Hopf son los únicos toros llanos lorentzianos inmersos en una amplia familia de sumersiones de Killing lorentzianas tridimensionales.A classical problem in Lorentzian geometry is the description of the isometric immersions between Lorentzian spaces of constant curvature. We investigate the problem of classifying the isometric immersion from the Lorentz plane into the three-dimensional anti-de Sitter space, providing a representation formula of these isometric immersions in terms of pairs of curves (possibly with singularities) in the hyperbolic plane. We then give an answer to the open problems proposed by Dajczer and Nomizu in 1981. Among all isometric immersions of the Lorentz plane into the anti-de Sitter space, some of them are actually Lorentzian tori (the basic examples are the Hopf tori). As an application of our previous description, we prove that any such torus can be recovered from two closed curves in the hyperbolic plane. Finally, we prove that Lorentzian Hopf tori are the only immersed Lorentzian flat tori in a wide family of Lorentzian three-dimensional Killing submersions.
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Leitner, Felipe. "The twistor equation in Lorentzian spin geometry." Doctoral thesis, [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=965107566.
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Bär, Christian, and Nicolas Ginoux. "Classical and quantum fields on Lorentzian manifolds." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5997/.
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We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
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Suhr, Stefan [Verfasser]. "Maximal geodesics in Lorentzian geometry / Stefan Suhr." Freiburg : Universität : Universitätsbibliothek Freiburg, 2010. http://d-nb.info/1008073687/34.
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Chen, Hao [Verfasser]. "Ball Packings and Lorentzian Discrete Geometry / Hao Chen." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1054637156/34.
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Saloom, Amani Hussain. "Curves in the Minkowski plane and Lorentzian surfaces." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/4451/.
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We investigate in this thesis the generic properties of curves in the Minkowski plane R2 1 and of smooth Lorentzian surfaces. The generic properties of curves in R2 1 are obtained by studying the contacts of curves in R2 1 with lines and pseudo-circles. These contacts are captured by the singularities of the families of height and distancesquared functions on the curves. On the other hand, the generic properties of smooth Lorentzian surfaces are obtained by studying certain Binary Differential Equations defined on the surfaces.
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Larssson, Eric. "Lorentzian Cobordisms, Compact Horizons and the Generic Condition." Thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-146276.
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We consider the problem of determining which conditions are necessaryfor cobordisms to admit Lorentzian metrics with certain properties. Inparticular, we prove a result originally due to Tipler without a smoothnesshypothesis necessary in the original proof. In doing this, we prove thatcompact horizons in a smooth spacetime satisfying the null energy condition aresmooth. We also prove that the ”generic condition” is indeed generic in the setof Lorentzian metrics on a given manifold
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Hernández, José Javier Cerda. "Ising and Potts model coupled to Lorentzian triangulations." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-18032015-170430/.
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The main objective of the present thesis is to investigate: What are the properties of the Ising and Potts model coupled to a CDT emsemble? For that objective, we used two methods: (1) transfer matrix formalism and Krein-Rutman theory. (2) FK representation of the q -state Potts model on CDTs and dual CDTs. Transfer matrix formalism permite us to obtain spectral properties of the transfer matrix using the Krein-Rutman theorem [KR48] on operators preserving the cone of positive func- tions. This yields results on convergence and asymptotic properties of the partition function and the Gibbs measure and allows us to determine regions in the parameter quarter-plane where the free energy converges. Second methods permite us to determine a region in the quadrant of parameters , > 0 where the critical curve for the classical model can be located. We also provide lower and upper bounds for the innite-volume free energy. Finally, using arguments of duality on graph theory and hight-T expansion we study the Potts model coupled to CDTs. This approach permite us to improve the results obtained for Ising model and obtain lower and upper bounds for the critical curve and free energy. Moreover, we obtain an approximation of the maximal eigenvalue of the transfer matrix at lower temperature.O objetivo principal da presente tese é pesquisar : Quais são as propriedades do modelo de Ising e Potts acoplado ao emsemble de CDT? Para estudar o modelo usamos dois métodos: (1) Matriz de transferência e Teorema de Krein-Rutman. (2) Representação FK para o modelo de Potts sobre CDT e dual de CDT. Matriz de transferência permite obter propriedades espectrais da Matriz de transferência utilizando o Teorema de Krein-Rutman [KR48] sobre operadores que conservam o cone de funções positivas. Também obtemos propriedades asintóticas da função de partição e das medidas de Gibbs. Esses propriedades permitem obter uma região onde a energia livre converge. O segundo método permite obter uma região onde a curva crítica do modelo pode estar localizada. Além disso, também obtemos uma cota superior e inferior para a energia livre a volume infinito. Finalmente, utilizando argumentos de dualidade em grafos e expansão em alta temperatura estudamos o modelo de Potts acoplado as triangulações causais. Essa abordagem permite generalizar o modelo, melhorar os resultados obtidos para o modelo de Ising e obter novas cotas, superior e inferior, para a energia livre e para a curva crítica. Além disso, obtemos uma aproximação do autovalor maximal do operador de transferência a baixa temperatura.
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Svensson, Maximilian. "On the Construction and Traversability of Lorentzian Wormholes." Thesis, Uppsala universitet, Teoretisk fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388473.
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In this literature review we discus and describe the theoretically predicted phenomena known as wormholes, where two different regions of space-time are joined by a “throat” or a “bridge”. If information or even an observer could be sent through the wormhole we refer to it as traversable. We argue that traversable wormholes demands negative energy densities and display a number of different constructions found within the field. Among these the orgional construction by EinsteinRosen and Morris-Thornes discussion on traversability. We also give a overview of the current state of the field by presenting to more recently published papers: “Casimir Energy of a Long Wormhole Throat” av Luke Buther och “Traversable Wormholes via a Double Trace Deformation” av Ping Gao, Daniel Louis Jafferis och Aron C.Wall.
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Grotz, Andreas [Verfasser], and Felix [Akademischer Betreuer] Finster. "A Lorentzian quantum geometry / Andreas Grotz. Betreuer: Felix Finster." Regensburg : Universitätsbibliothek Regensburg, 2011. http://d-nb.info/1023282259/34.
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Bin, Turki Nasser. "Fundamental domains for left-right actions in Lorentzian geometry." Thesis, University of Liverpool, 2014. http://livrepository.liverpool.ac.uk/2003726/.
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We consider tilde{G} = tilde{SU}(1, 1) = tilde{SL}(2,R). The aim of this thesis is to compute the fundamental domains for two series of groups of the form tilde{Gamma}_1 X tilde{Gamma}_2 acting on tilde{G} by left-right multiplication,i.e. (g, h) . x = gxh^{−1}, where tilde{Gamma}_1 and tilde{Gamma}_2 are discrete subgroups of tilde{G} of the same finite level and tilde{Gamma}_2 is cyclic. The level of a subgroup tilde{Gamma} in tilde{G} is defined as the index of the group tilde{Gamma} intersection with Z(tilde{G}) in the center Z(tilde{G}) =� Z. From computing the fundamental domain we can describe the biquotients tilde{Gamma}_1 \ tilde{G} / tilde{Gamma}_2 which are diffeomorphic to the links of certain quasihomogeneous Q-Gorenstein surface singularities, i.e. the intersections of the singular variety with suffi�ciently small spheres around the isolated singular point as shown in [16].
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Schemel, Peter. "On the singularitys set of Lorentzian almost Einstein structures." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17546.
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Eine almost Einstein-Struktur (M,g,sigma) ist eine n-dimensionale zusammenhängende Mannigfaltigkeit M mit einer pseudo-riemannschen Metrik g und einer glatten Skalenfunktion sigma deren almost Einstein-Tensor A[g,sigma] (der spurfreie Anteil von Hess[g] sigma + sigma P[g], wobei P[g] den Schouten-Tensor bezeichnet) verschwindet. Sie verallgemeinert die Idee einer Einsteinmannigfaltigkeit in dem Sinne, dass die konform geänderte Metrik 1/sigma^2 g außerhalb der Nullstellenmenge Sigma = sigma^(-1)(0) eine Einstein-Metrik ist. Ziel dieser Doktorarbeit ist es, ein detailiertes Bild von Sigma in Lorentzsignatur (-+...+) zu erhalten. Teil dieser Arbeit ist zudem eine indexfreie Darstellung ausgewählter Resultate für konform kompaktifizierbare Einsteinmannigfaltigkeiten in Lorentzsignatur im Rahmen von almost Einstein-Strukturen. Diese Umformulierung wird dann benutzt, um eine Verallgemeinerung der konformen Wellengleichungen für beliebige gerade Dimensionen n = 2m > 4 vorzuschlagen.An almost Einstein structure (M,g,sigma) is an n-dimensional connected manifold M equipped with a pseudo-Riemannian metric g and a scale factor sigma in C^infty(M) such that the almost Einstein tensor A[g,sigma] (the trace-free part of Hess[g] sigma + sigma P[g], with Schouten tensor P[g]) vanishes. It generalises the idea of an Einstein manifold in the way that 1/sigma^2 g is an Einstein metric away from the singularity set Sigma = sigma^(-1)(0). The purpose of this thesis is to get a detailed picture of Sigma in Lorentzian signature (-+...+). Part of this thesis is also an index-free survey of selected results on conformally compact Einstein manifolds in Lorentzian signature in the framework of almost Einstein structures. This reformulation is used to suggest a generalisation of the conformal wave equations to arbitrary even dimensions n = 2m > 4.
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Davids, Stefan. "A state sum model for (2+1) Lorentzian quantum gravity." Thesis, University of Nottingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391393.
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Schliebner, Daniel. "Contributions to the geometry of Lorentzian manifolds with special holonomy." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17185.
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In dieser Arbeit studieren wir Lorentz-Mannigfaltigkeiten mit spezieller Holonomie, d.h. ihre Holonomiedarstellung wirkt schwach-irreduzibel aber nicht irreduzibel. Aufgrund der schwachen Irreduzibilität lässt die Darstellung einen ausgearteten Unterraum invariant und damit also auch eine lichtartige Linie. Geometrisch hat dies zur Folge, dass wir zwei parallele Unterbündel (die Linie und ihr orthogonales Komplement) des Tangentialbündels erhalten. Diese Arbeit nutzt diese und weitere Objekte um zu beweisen, dass kompakte Lorentzmannigfaltigkeiten mit Abelscher Holonomie geodätisch vollständig sind. Zudem werden Lorentzmannigfaltigkeiten mit spezieller Holonomie und nicht-negativer Ricci-Krümung auf den Blättern der Blätterung, induziert durch das orthogonale Komplement der parellelen Linie, und maximaler erster Bettizahl untersucht. Schließlich werden vollständige Ricci-flache Lorentzmannigfaltigkeiten mit vorgegebener voller Holonomie konstruiert.In the present thesis we study dimensional Lorentzian manifolds with special holonomy, i.e. such that their holonomy representation acts indecomposably but non-irreducibly. Being indecomposable, their holonomy group leaves invariant a degenerate subspace and thus a light-like line. Geometrically, this means that, since being holonomy invariant, this line gives rise to parallel subbundles of the tangent bundle. The thesis uses these and other objects to prove that Lorentian manifolds with Abelian holonomy are geodesically complete. Moreover, we study Lorentzian manifolds with special holonomy and non-negative Ricci curvature on the leaves of the foliation induced by the orthogonal complement of the parallel light-like line whose first Betti number is maximal. Finally, we provide examples of geodesically complete and Ricci-flat Lorentzian manifolds with special holonomy and prescribed full holonomy group.
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Dirmeier, Alexander [Verfasser], and Mike [Akademischer Betreuer] Scherfner. "Particular Timelike Flows in Global Lorentzian Geometry / Alexander Dirmeier. Betreuer: Mike Scherfner." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1032693398/34.
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Dirmeier, Alexander Verfasser], and Mike [Akademischer Betreuer] [Scherfner. "Particular Timelike Flows in Global Lorentzian Geometry / Alexander Dirmeier. Betreuer: Mike Scherfner." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-38530.
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JÃnior, Eraldo Almeida Lima. "Uniqueness for hypersurfaces immersed on riemannian and lorentzian spaces: results, examples and counter-examples." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14590.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoCoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
In this work we present uniqueness results for constant mean curvature hypersurfaces in Riemannian and Lorentzian products. We dealt with product whose fiber has sectional curvature bounded from below. We considered a certain control in the norm of the gradient of the height function by the norm of the second fundamental form in order to obtain that such a surface is slice. We also obtained uniqueness through integrability conditions in the gradient of the height function. We also presented an extension of a lemma due to Nishikawa which was used to prove the results for the case of maximal surfaces, that is, with zero mean curvature. We have utilized as an essential tool, in the prove of the results, the generalized Omori-Yau maximum principle in one of the latest versions. In the end, we present examples showing and justifying the necessity of required hypothesis in the results.
Neste trabalho, apresentamos resultados de unicidade para hipersuperfÃcies de curvatura mÃdia constante, tanto em um produto Riemanniano como Lorentziano. Tratamos de produtos cuja fibra tenha curvatura seccional limitada por baixo. Para isto, consideramosum certo controle na norma do gradiente da funÃÃo altura pela norma da segunda forma fundamental com o objetivo de obter que tal hipersuperfÃcie deve ser um slice, i.e., uma "fatia". TambÃm obtemos a unicidade atravÃs de condiÃÃes de integrabilidade no gradiente da funÃÃo altura. Apresentamos uma extensÃo de um lema devido a Nishikawa que utilizamos para provar os resultados no caso das superfÃcies mÃximas, ou seja, aquelas com curvatura mÃdia nula. Utilizamos como ferramenta essencial, na prova dos resultados, o princÃpio do mÃximo generalizado de Omori-Yau em suas versÃes mais atuais. Finalmente, apresentamos exemplos que justificam a necessidade das hipÃteses exigidas nos resultados.
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Freire, Emanoel Mateus dos Santos. "Representação de Weierstrass em variedades Riemannianas e Lorentzianas." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30102018-145548/.
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O Teorema de Representação de Weierstrass clássico, que faz uso da análise complexa para descrever uma superfície mínima imersa no espaço Euclidiano em termos de dados holomorfos, tem sido extremamente útil seja para construir novos exemplos de superfícies mínimas, seja para o estudo das propriedades destas superfícies. Em [24], usando a equação harmônica, os autores determinam uma fórmula de representação para superfícies mínimas, simplesmente conexas, imersas em uma variedade Riemanniana qualquer. Neste caso, a condição de holomorficidade dos dados de Weierstrass consiste em um sistema de equações diferenciais parciais com coeficientes não constantes. Logo, em geral, é complicado determinar soluções explícitas. No entanto, escolhendo adequadamente o espaço ambiente, tais equações se simplificam e a fórmula pode ser usada para produzir novos exemplos de imersões mínimas conformes. No espaço de Lorentz-Minkowski tridimensional uma fórmula de representação tipo-Weierstrass foi provada por Kobayashi, para o caso das imersões mínimas de tipo espaço (ver [18]), e por Konderak no caso das imersões mínimas de tipo tempo (ver [20]). Na demonstração destas fórmulas se utilizam as ferramentas da análise complexa e paracomplexa, respectivamente. Recentemente, em [22] os resultados de Kobayashi e Konderak foram generalizados para o caso de superfícies mínimas (de tipo espaço e de tipo tempo) imersas em 3-variedades Lorentzianas. Nesta dissertação estudaremos as fórmulas de representação de Weierstrass para superfícies mínimas imersas em variedades Riemannianas e Lorentzianas, que foram obtidas nos artigos [18], [20], [22] e [24].The classic Weierstrass Representation Theorem, which makes use of complex analysis to describe a minimal surface immersed in the Euclidean space in terms of holomorphic data, has been extremely useful either to construct new examples of minimal surfaces, rather than to study structural properties of these surfaces. In [24], using the standard harmonic equation, the authors determine a representation formula for simply connected immersed minimal surfaces in a Riemannian manifold. In this case, the holomorphicity condition of the Weierstrass data is a system of partial differential equations with nonconstant coefficients. Therefore, in geral, it is very difficult to determine explicit solutions. However, for particular ambient spaces, these equations become simpler and the formula can be used to produce new examples of conformal minimal immersions. In the three-dimensional Lorentz-Minkowski space a Weierstrass-type representation formula was proved by Kobayashi for spacelike minimal immersions (see [18]), and by Konderak for the case of timelike minimal immersions (see [20]). In the demonstration of these formulas are used the tools of complex and paracomplex analysis, respectively. Recently, in [22] the results of Kobayashi and Konderak were generalized to the case of (spacelike and timelike) minimal surfaces immersed in 3-Lorentzian manifolds. In this dissertation, we will study the Weierstrass representation formula for immersed minimal surfaces in Riemannian and Lorentzian manifolds, that was obtained in the articles [18], [20], [22] and [24].
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Turkalj, Ivica [Verfasser], Rudolf [Akademischer Betreuer] Scharlau, and Detlev [Gutachter] Hoffmann. "Reflective Lorentzian lattices of signature (5, 1) / Ivica Turkalj ; Gutachter: Detlev Hoffmann ; Betreuer: Rudolf Scharlau." Dortmund : Universitätsbibliothek Dortmund, 2017. http://d-nb.info/1139892533/34.
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Tuerxunjiang, Abulikemu. "FDTD measurement of the reflection coefficient associated with total internal reflection from gainy Lorentzian media." Pullman, Wash. : Washington State University, 2008. http://www.dissertations.wsu.edu/Thesis/Fall2008/A_Tuerxunjiang_120108.pdf.
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Thesis (M.S. in physics)--Washington State University, December 2008.Title from PDF title page (viewed on July 10, 2009). "Department of Physics and Astronomy." Includes bibliographical references (p. 64-68).
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Chen, Xiaopei. "Ultra-Narrow Laser Linewidth Measurement." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11124.
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In this report, we give a deeper investigation of the loss-compensated recirculating delayed self-heterodyne interferometer (LC-RDSHI) for ultra-narrow linewidth measurement, including the theoretical analysis, experimental implementation, further modification on the system and more applications.
Recently, less than 1kHz linewidth fiber lasers have been commercialized. But even the manufacturers face a challenge on accurately measuring the linewidth of such lasers. There is a need to develop more accurate methods to characterize ultra-narrow laser linewidth and frequency noises.
Compared with other currently available linewidth measurement techniques, the loss-compensated recirculating delayed-heterodyne interferometer (LC-RDSHI) technique is the most promising one. It overcomes the bottle-neck of the high resolution requirement on the delayed self-heterodyne interferometer (DSHI) by using a short length of fiber delay line. This method does not need another narrower and more stable laser as the reference which is the necessary component in heterodyne detection. The laser spectral lineshape can be observed directly instead of complicated interpretation in frequency discriminator techniques.
The theoretical analysis of a LC-RDSHI gives us a guidance on choosing the optimal parameters of the system and assists us to interpret the recorded spectral lineshape. Laser linewidth as narrow as 700Hz has been proved to be measurable by using the LC-RDSHI method.
The non-linear curve fitting of Voigt lineshape to separate Lorentzian and Gaussian components was investigated. Voigt curve fitting results give us a clear view on laser frequency noises and laser linewidth nature. It is also shown that for a ultra-narrow linewidth laser, simply taking 20dB down from the maximum value of the beat spectrum and dividing by $2\sqrt{99}$ will over estimate the laser linewidth and coherent length.
Besides laser linewidth measurement in the frequency domain, we also implemented time-domain frequency noise measurement by using a LC-RDSHI. The long fiber delay obtained by a fiber recirculating loop provides a higher resolution of frequency noise measurement.
However, spectral width broadening due to fiber nonlinearity, environmental perturbations and laser intrinsic 1/f frequency noises are still potential problems in the LC-RDSHI method. A new method by adding a transmitter switch and a loop switch is proposed to minimize the Kerr effect caused by multiple recirculation.Ph. D.
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Schemel, Peter [Verfasser], Helga [Gutachter] Baum, Andreas [Gutachter] Juhl, and Lars [Gutachter] Andersson. "On the singularitys set of Lorentzian almost Einstein structures / Peter Schemel. Gutachter: Helga Baum ; Andreas Juhl ; Lars Andersson." Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://d-nb.info/1109846231/34.
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Schliebner, Daniel [Verfasser], Helga [Akademischer Betreuer] Baum, Miguel Sánchez [Akademischer Betreuer] Caja, and Charles [Akademischer Betreuer] Frances. "Contributions to the geometry of Lorentzian manifolds with special holonomy / Daniel Schliebner. Gutachter: Helga Baum ; Miguel Sánchez Caja ; Charles Frances." Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://d-nb.info/1069896152/34.
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Cuzzola, Angelo. "Aspects of supergeometry in locally covariant quantum field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10391/.
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In questa tesi vengono presentati i piu recenti risultati relativi all'estensione della teoria dei campi localmente covariante a geometrie che permettano di descrivere teorie di campo supersimmetriche. In particolare, si mostra come la definizione assiomatica possa essere generalizzata, mettendo in evidenza le problematiche rilevanti e le tecniche utilizzate in letteratura per giungere ad una loro risoluzione. Dopo un'introduzione alle strutture matematiche di base, varieta Lorentziane e operatori Green-iperbolici, viene definita l'algebra delle osservabili per la teoria quantistica del campo scalare. Quindi, costruendo un funtore dalla categoria degli spazio-tempo globalmente iperbolici alla categoria delle *-algebre, lo stesso schema viene proposto per le teorie di campo bosoniche, purche definite da un operatore Green-iperbolico su uno spazio-tempo globalmente iperbolico. Si procede con lo studio delle supervarieta e alla definizione delle geometrie di background per le super teorie di campo: le strutture di super-Cartan. Associando canonicamente ad ognuna di esse uno spazio-tempo ridotto, si introduce la categoria delle strutture di super-Cartan (ghsCart) il cui spazio-tempo ridotto e globalmente iperbolico. Quindi, si mostra, in breve, come e possibile costruire un funtore da una sottocategoria di ghsCart alla categoria delle super *-algebre e si conclude presentando l'applicazione dei risultati esposti al caso delle strutture di super-Cartan in dimensione 2|2.
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Mehidi, Lilia. "Points conjugués des tores lorentziens." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0295.
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Dans la première partie de cette thèse, nous donnons une description des surfaces lorentziennes simplement connexes et maximales dont le groupe d’isométries est de dimension 1 (c’est-à-dire possédant un champ de Killing complet), à l’aide d’une variété riemannienne de dimension 1 (généralement non séparée) et d’une fonction lisse définie dessus ; nous étudions ensuite la complétude géodésique de telles surfaces. Dans la deuxième partie qui est la partie principale de cette thèse, nous donnons une infinité de nouveaux exemples de surfaces lorentziennes compactes sans points conjugués. De plus, nous étudions l’existence et la stabilité de cette propriété parmi les métriques lorentziennes admettant un champ de Killing. Nous obtenons une nouvelle obstruction et prouvons que le tore de Clifton-Pohl et certains de nos exemples sont aussi stables que possible. Cela montre que, contrairement au théorème de Hopf riemannien, l’absence de points conjugués dans le cadre de Lorentzian n’est ni "spéciale" ni rigideIn the first part of this thesis, we give a description of simply connected maximal Lorentzian surfaces whose group of isometries is of dimension 1 (i.e. with a complete Killing field), in terms of a 1-dimensional generally non-Hausdorff Riemannian manifold and a smooth function defined there. Next, we study the geodesic completeness of such surfaces. In the second part which is the main part of this thesis, we give infinitely many new examples of compact Lorentzian surfaces without conjugate points. Further, we study the existence and the stability of this property among Lorentzian metrics with a Killing field. We obtain a new obstruction and prove that the Clifton- Pohl torus and some of our examples are as stable as possible. This shows that in constrast with the Riemannian Hopf theorem, the absence of conjugate points in the Lorentzian setting is neither "special" nor rigid
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LIMA, JÚNIOR Eraldo Almeida. "Resultados do tipo Calabi-Bernstein em −R × Hn." Universidade Federal de Campina Grande, 2011. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1244.
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Neste trabalho, apresentamos um estudo das hipersuperfícies tipo-espaço imersas no ambiente −R × Hn, exibindo condições para que tais hipersuperfícies sejam slices {t0}×Hn. Para uma melhor compreensão das demonstrações e dos resultados, inserimos processos de diferenciação, cálculos de gradientes e Laplacianos que, juntamente com o princípio do máximo de Omori-Yau, foram cruciais no desenvolvimento dos resultados que, em sua maioria são do tipo Bernstein. Também incluímos um resultado do tipo Calabi.
In this work we present a study of the spacelike hypersurfaces immersed in the manifold −R × Hn providing sufficient conditions for such hypersurfaces be slices, {t0}×Hn. For a better understanding of the proofs and results, we have added differentiation processes, gradient computations and Laplacians which jointly with the Omori-Yau Maximum Principle were crucial in the developing of the results whose are mostly Bernstein-type. In the elapsing we also included Calabi-type results.
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Labeni, Hicham. "Réalisation de métrique CAT(k) sur les surfaces dans les variétés lorentziennes de courbure constante." Thesis, CY Cergy Paris Université, 2020. http://www.theses.fr/2020CYUN1007.
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On prouve que toute métrique de courbure leq k (au sens de A. D. Alexandrov) sur une surface fermée est isométrique à une métrique induite sur une surface convexe dans un espace lorentzien de dimension 3 et de courbure sectionnelle constante kWe prove that any metric with curvature leq k (in the sense of A. D. Alexandrov) on a closed surface is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension 3 with sectional curvature k
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Nicotra, Alessandro. "Analytical map between EPRL spin foam models in loop quantum gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23179/.
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Loop Quantum Gravity (LQG) is one of the theoretical frameworks attempting to build a quantum theory of gravitation.
Spin Foam theory provides a regularized, background-independent, and Lorentz covariant path integral for the transition amplitudes between LQG kinematical states.
The state of the art of the theory is the EPRL model, formulated with the Euclidean and the Lorentzian signatures. They differ by their gauge group structures, which are respectively SO(4,R) and SO(1,3).
The first is a compact group: it has finite-dimensional unitary irreducible representations, and the integral on the group manifold is simple. The second is non-compact. Therefore, the computations in the Lorentzian EPRL model are more complicated than in the Euclidean one. The Euclidean model is the preferred choice for physical calculations. Given their similarities it has been so far assumed, as a strong hypothesis, that the results obtained in the Euclidean model also hold for the Lorentzian one.
This work's primary goal is to present the main characteristics of the models and a set of prescriptions to map the structure and, at least in a qualitative way, the results obtained in the Euclidean model into the Lorentzian one.
Chapter 1 provides an overview of the basic ingredients of the discussion: General Relativity, BF theories and LQG transition amplitudes between quantum states of spacetime.
Chapters 2 and 3 are respectively a description of the Euclidean and Lorentzian EPRL models, from the representation theory of their gauge groups to the construction of the EPRL transition amplitudes.
Chapter 4 portrays the current state of research in EPRL Spin Foam theory, with a qualitative description of the main results achieved in both models.
The main topic of the thesis and my original work is contained in Chapter 5, in which, from a set of prescriptions, the group structure of the Euclidean model is mapped into the Lorentzian one, allowing a comparison between the transition amplitudes.
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Prabhu, G. Radhakrishna. "Studies On Surface Plasmon Resonance And Related Experimental Methods Using Fixed Plasmon Angle." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/205.
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Surface plasmon waves are transverse magnetic electromagnetic waves propagating along a dielectric-metal interface. These waves can be excited by resonant absorption of electromagnetic radiation leading to surface plasmon resonance (SPR) at the interface. The resonance is characterised by a reduction in the intensity of the reflected light at the interface due to strong coupling of incident optical radiation to surface plasmons. This gives rise to a minimum at a sharply defined angle of incidence, referred to as SPR angle or plasmon angle. The phenomenon of SPR has been extensively used in the past to develop reflective type optical devices for sensing applications on account of the high dielectric function dependent sensitivity of the SPR angle. Basically, devices which exhibit this phenomenon have a structure consisting of a metal film sandwiched between two dielectrics. The reflectivity of such a device is theoretically modelled based on either theory of thin films (Fresnel's model) or theory of resonance (Lorentzian model). These models have very effectively predicted the behaviour of such devices based on the shift in SPR angle due to the dielectric function variations.
We have been investigating the SPR device for intensity based metrological applications utilising its high angular sensitive reflectivity, with fixed SPR angle. In these intensity based applications or measurements, direct and simple expressions connecting intensity variation to angular change are unavailable in the literature and quantitative estimation or data inversion is based on either curve fitting or iterative methods. Fresnel and Lorentzian models have commonly been used in the experiments but data inversion through the Fresnel model is computationally complex and the Lorentzian model, although less complicated, gives erroneous results due to its approximate nature. In order to obtain a simple expression between intensity variation and the angular change, we have re-looked at the two existing models in order to derive an expression which has the simplicity of the Lorentzian model and the accuracy of the Fresnel model in the experiments with fixed plasmon angles. These efforts have been particularly directed to understand the relationship between intensity variation and meteorologically important properties of such devices. This thesis is an attempt to summarize the computational results which have led us to some novel experimental methodologies which have been used to exploit these devices for inverse type, illumination specific, SPR based applications.
The work presented in this thesis is organised in six chapters. Chapter 1, gives an overview of optical sensing, theory of surface plasmons, excitation schemes for surface plasmons, development of the SPR device and its characterisation. It also includes a brief literature review in the area of surface plasmon resonance, covering both the theoretical and experimental aspects. The objectives of the work and the scope of the thesis are also presented.
Chapter 2 presents the existing models of SPR device, based on Fresnel's and the Lorentzian models. These models allow reflectance calculations from knowledge of either the optical parameters that describe the layers or the parameters of the waves that propagate through them. Using these models, the inverse problem of estimating either the angle of incidence or the optical constants of the layers of the sensors utilizing the intensity based measurements is generally difficult. In order to solve this problem where the plasmon angles are fixed, a modified formalism for the angle scanned SPR spectrum of a three-layered SPR sensor is presented in this chapter. The new formalism regroups the wave vector parameters of Lorentzian resonance theory into a set of non-dimensional parameters 1, 4K and R. The new reflectivity index (1), which is the ratio of reflectance to the absorptance, has been introduced to help explain the physical processes underlying the device operation in the high sensitivity region of the characteristics. The parameter 4Kis a constant of the device and it depends on the dielectric constants of the device. This is a new SPR index and is identified at a point where reflectance and absorptance match. Parameter R is related to the loss mechanisms in the device and will be explained in detail in Chapter 3. This simple model links the new reflectivity index (1) to the angular detune from SPR angle (ΔƟ) and it brings out a parabolic variation of ΔƟ with 1. In this chapter the mathematical derivation of the proposed model is presented and the significance of the new parameters 1, 4Kand Rare discussed.
Chapter 3 evaluates the characteristic nature of errors associated with the predictions from the proposed model and presents methods for neutralizing them. It is demonstrated with the help of the function K which is linearly dependant on 1, that the proposed model predicts the reflectance from the wave vector parameters as accurately as the Fresnel's model. This R parameter explains the slowly varying nature of the radiative loss with the angle of incidence and
this variation contributes significantly to the SPR characteristics. As a consequence, it is found that the SPR characteristics can be represented as a sum of two primary functions which are parabolic and linear, respectively, and this leads to the easy explanation of the SPR characteristics. The present chapter also discusses a new observation that the angle-scanned SPR spectrum can be accurately described using a straight line in intercept form. The intercept value depends on 4Kand the slope depends on K. In addition to this, this chapter discusses practical methods for estimation of the intercept and the slope of such a straight line which are functions of the key wave vector parameters. A detailed discussion on the proposed model highlighting its advantages for inverse type, illumination specific, SPR-based applications with fixed SPR angle is also presented.
Chapter 4 describes the applications of the proposed model for optical constant measurements. The first part highlights a new approach for the determination of the dielectric constants of the metal film used for the optimised- or nearly-optimised SPR sensors using the proposed model. In the complex dielectric constant, the real part is calculated from the SPR angle and the imaginary part from 4K. A discussion on the dielectric constant study of silver and gold metal film is presented. The advantages of the proposed approach such as its simplicity and direct methodology are then discussed. The second part of the chapter also proposes a new approach to carry out measurements on the absorbance of the medium with enhanced sensitivity utilising the parameter 4K It describes a computational study on the variation of 4K values with the dielectric function and highlights the relationship of 4K variation due to the imaginary part of the dielectric function (absorption) of the samples. The physical processes causing a change in the value of 4Kdue to absorption is also discussed along with some computational results.
Chapter 5 reports the study carried out to bring out the importance of the new index,4K in metrological applications. Based on the new model, the effect of the laser beam divergence on SPR curve is studied. This chapter first of all discusses the design of the SPR device and the new methods for the development and characterisation of such a device. Details of the experimental procedure for laser divergence evaluation are proposed along with some of the significant computational results. Furthermore, a few applications such as focal length measurement of optical lenses, micro-displacement measurement based on the divergence of the laser beam are also reported. Since the SPR characteristics can be represented easily using the new model, the angular dependent intensity variation can be utilised for some metrological applications with simple data processing. In this context, the high angular sensitivity of the SPR device is studied and some applications such as micro-displacement measurement, pressure measurement and optical wedge angle measurement are included to highlight the above advantages.
The last chapter, Chapter 6, gives a summary and conclusions of the work presented in the thesis. The scope for future investigations is also included in this chapter.
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Hassani, Masoud. "Study of cohomogeneity one three dimensional Einstein universe." Thesis, Avignon, 2018. http://www.theses.fr/2018AVIG0421/document.
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Dans cette thèse des actions conformes de cohomogénéité un sur l'univers d'Einstein tridimensionel sont classifiées. Notre stratégie est d'établir dans un premier temps quel peut être le groupe de transformations conformes impliqué, à conjugaison près. Nous décrivons aussi la topologie et la nature causale des orbites d'une telle actionIn this thesis, the conformal actions of cohomogeneity one on the three-dimensional Einstein universe are classified. Our strategy in this study is to determine the representation of the acting group in the group of conformal transformations of Einstein universe up to conjugacy. Also, we describe the topology and the causal character of the orbits induced by cohomogeneity one actions in Einstein universe
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Ribeiro, Pedro Lauridsen. "Aspectos estruturais e dinâmicos da correspondência AdS/CFT: Uma abordagem rigorosa." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14012008-131931/.
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Elaboramos um estudo detalhado de alguns aspectos d(e uma versão d)a correspondência AdS/CFT, conjeturada por Maldacena e Witten, entre teorias quânticas de campo num fundo gravitacional dado por um espaço-tempo assintoticamente anti-de Sitter (AAdS), e teorias quânticas de campos conformalmente covariantes no infinito conforme (no sentido de Penrose) deste espaço-tempo, aspectos estes: (a) independentes d(o par d)e modelos específicos em Teoria Quântica de Campos, e (b) suscetíveis a uma reformulação em moldes matematicamente rigorosos. Adotamos como ponto de partida o teorema demonstrado por Rehren no contexto da Física Quântica Local (também conhecida como Teoria Quântica de Campos Algébrica) em espaços-tempos anti-de Sitter (AdS), denominado holografia algébrica ou dualidade de Rehren. O corpo do presente trabalho consiste em estender o resultado de Rehren para uma classe razoavelmente geral de espaços-tempos AAdS d-dimensionais (d>3), escrutinar como as propriedades desta extensão são enfraquecidas e/ou modificadas em relação ao espaço-tempo AdS, e como efeitos gravitacionais não-triviais se manifestam na teoria quântica no infinito conforme. Dentre os resultados obtidos, citamos: condições razoavelmente gerais sobre geodésicas nulas no interior (cuja plausibilidade justificamos por meio de resultados de rigidez geométrica) não só garantem que a nossa generalização é geometricamente consistente com causalidade, como também permite uma reconstrução ``holográfica\'\' da topologia do interior na ausência de horizontes e singularidades; a implementação das simetrias conformes na fronteira, que associamos explicitamente a uma família de isometrias assintóticas do interior construída de maneira intrínseca, ocorre num caráter puramente assintótico e é atingida dinamicamente por um processo de retorno ao equilíbrio, mediante condições de contorno adequadas no infinito; efeitos gravitacionais podem eventualmente causar obstruções à reconstrução da teoria quântica no interior, ou por torná-la trivial em regiões suficientemente pequenas ou devido à existência de múltiplos vácuos inequivalentes, que por sua vez levam à existência de excitações solitônicas localizadas ao redor de paredes de domínio no interior, similares a D-branas. As demonstrações fazem uso extensivo de geometria Lorentziana global. A linguagem empregada para as teorias quânticas relevantes para nossa generalização da dualidade de Rehren segue a formulação funtorial de Brunetti, Fredenhagen e Verch para a Física Quântica Local, estendida posteriormente por Sommer para incorporar condições de contorno.We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter\'s conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren\'s result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity\'s quantum theory. Among the obtained results, we quote: not only does the imposition of reasonably general conditions on bulk null geodesics (whose plausibility we justify through geometrical rigidity techniques) guarantee that our generalization is geometrically consistent with causality, but it also allows a ``holographic\'\' reconstruction of the bulk topology in the absence of horizons and singularities; the implementation of conformal symmetries in the boundary, which we explicitly associate to an intrinsically constructed family of bulk asymptotic isometries, have a purely asymptotic character and is dynamically attained through a process of return to equilibrium, given suitable boundary conditions at infinity; gravitational effects may cause obstructions to the reconstruction of the bulk quantum theory, either by making the latter trivial in sufficiently small regions or due to the existence of multiple inequivalent vacua, which on their turn lead to the existence of solitonic excitations localized around domain walls, similar to D-branes. The proofs make extensive use of global Lorentzian geometry. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions. (An English translation of the full text can be found at arXiv:0712.0401)
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Vasconcellos, João Braga de Góes e. "Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-31052016-103235/.
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Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.In this thesis we present a both mathematical and conceptually rigorous quantization method for the neutral scalar field free of interactions. Initially, we introduce some aspects of the Theory of Distributions and we establish some points of Lorentzian geometry. The rest of the work is divided in two parts: in the first one, we study wave equations on globally hyperbolic Lorentzian manifolds, hence presenting the concept of fundamental solutions within the context of locally defined wave equations. Next, we progressively construct fundamental solutions for the wave operator from the Riesz distribution. Once established a solution to the wave equation in a neighbourhood of a point of the manifold, we move forward to produce a global solution from the extension of the Cauchy problem to the whole manifold. At this stage, fundamental solutions are replaced by Green\'s operators by the imposition of appropriate boundary conditions. In the last part, we present a minimum on the Theory of Categories and Functors. This is followed by the use of this formalism in the development of a second-quantization functor between the category of Lorentzian globally hyperbolic manifolds and the category of nets of C*-algebras obeying Haag-Kastler axioms. Finally, we turn our attention to the particular case of the quantum free scalar field.
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Lärz, Kordian. "Global aspects of holonomy in pseudo-Riemannian geometry." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16363.
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In dieser Arbeit untersuchen wir die Interaktion von Holonomie und der globalen Geometrie von Lorentzmannigfaltigkeiten und pseudo-Riemannschen Untermannigfaltigkeiten in Räumen konstanter Krümmung. Insbesondere konstruieren wir schwach irreduzible, reduzible Lorentzmetriken auf den Totalräumen von gewissen Kreisbündeln, was zu einer Konstruktionsmethode von Lorentzmannigfaltigkeiten mit vorgegebener Holonomiedarstellung führt. Danach führen wir eine Bochnertechnik für die Lorentzmannigfaltigkeiten ein, die ein nirgends verschwindendes, paralleles, lichtartiges Vektorfeld zulassen, dessen orthogonale Distribution kompakte Blätter hat. Schließlich klassifizieren wir normale Holonomiedarstellungen von raumartigen Untermannigfaltigkeiten in Räumen konstanter Krümmung und verallgemeinern die Klassifikation eine größere Klasse von Untermannigfaltigkeiten.In this thesis we study the interaction of holonomy and the global geometry of Lorentzian manifolds and pseudo-Riemannian submanifolds in spaces of constant curvature. In particular, we construct weakly irreducible, reducible Lorentzian metrics on the total spaces of certain circle bundles leading to a construction of Lorentzian manifolds with specified holonomy representations. Then we introduce a Bochner technique for Lorentzian manifolds admitting a nowhere vanishing parallel lightlike vector field whose orthogonal distribution has compact leaves. Finally, we classify normal holonomy representations of spacelike submanifolds in spaces of constant curvature and extend the classification to more general submanifolds.
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Cortier, Julien. "Etude mathématique de trous noirs et de leurs données initiales en relativité générale." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20068/document.
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L'objet de cette thèse est l'étude mathématique de familles d'espaces-temps satisfaisant aux équations d'Einstein de la Relativité Générale. Deux approches sont considérées pour cette étude. La première partie, composée des trois premiers chapitres, examine les propriétés géométriques des espaces-temps d'Emparan-Reall et dePomeransky-Senkov, de dimension 5. Nous montrons qu'ils contiennent un trou noir, dont l'horizon des événements est à sections compactes non-homéomorphes à la sphère. Nous en construisons une extension analytique et prouvons que cette extension est maximale et unique dans une certaine classe d'extensions pour les espaces-temps d'Emparan-Reall. Nous établissons ensuite le diagramme de Carter-Penrose de ces extensions, puis analysons la structure de l'ergosurface des espaces-temps de Pomeransky-Senkov. La deuxième partie est consacrée à l'étude de données initiales, solutions des équations des contraintes, induites par les équations d'Einstein. Nous effectuons un recollement d'une classe de données initiales avec des données initiales d'espaces-temps de Kerr-Kottler-deSitter, en utilisant la méthode de Corvino. Nous construisons, d'autre part, des métriques asymptotiquement hyperboliques en dimension 3, satisfaisant les hypothèses du théorème de masse positive à l'exception de la complétude, et ayant un vecteur moment-énergie de genre causal arbitraireThe aim of this thesis is the mathematical study of families of spacetimes satisfying the Einstein's equations of General Relativity. Two methodsare used in this context.The first part, consisting of the first three chapters of this work,investigates the geometric properties of the Emparan-Reall andPomeransky-Senkov families of 5-dimensional spacetimes. We show that they contain a black-hole region, whose event horizon has non-spherical compact cross sections. We construct an analytic extension, and show its maximality and its uniqueness within a natural class in the Emparan-Reallcase. We further establish the Carter-Penrose diagram for these extensions, and analyse the structure of the ergosurface of the Pomeransky-Senkovspacetimes.The second part focuses on the study of initial data, solutions of theconstraint equations induced by the Einstein's equations. We perform agluing construction between a given family of inital data sets andinitial data of Kerr-Kottler-de Sitter spacetimes, using Corvino'smethod.On the other hand, we construct 3-dimensional asymptotically hyperbolicmetrics which satisfy all the assumptions of the positive mass theorem but the completeness, and which display an energy-momentum vector of arbitry causal type
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Figueiredo, Vera Lucia Xavier 1948. "Estrutura spinorial em variedades lorentzianas." [s.n.], 1987. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306696.
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Orientador: Waldyr A. Rodrigues JuniorTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Ciencia da Computação
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Resumo: Este trabalho tem dois objetivos principais. O primeiro consiste em eslcarecer as diferentes definições e representações de spinores que aparecem na literatura, a saber: Spinores covariantes (c-spinor) definidos como elementos de espaços vetoriais complexos, munidos de um "produto escalar" que não invariantes sob a ação de certos grupos Lie ...Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital
Abstract: This thesis have two main purposes. The first is to clear up the different definitions and representations of spinors appearing in the literature. These are: covafitant iptnofiA (c-spinors) defined as elements of complex vector spaces equiped with a "scalar product" which are invariant under the action of certain Lie groups ...Note: The complete abstract is available with the full electronic digital thesis or dissertations
Doutorado
Doutor em Matemática
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Cintra, Adriana Araujo 1985. "Superfícies mínimas em variedades lorentzianas." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307110.
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Orientadores: Francesco Mercuri, Irene Ignazia OnnisTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Nesta tese estudamos as superfícies mínimas imersas em variedades Lorentzianas. Desenvolvemos uma versão geral da fórmula da representação de Weierstrass para superfícies mínimas do tipo tempo e tipo espaço imersas em uma variedade Lorentziana n-dimensional. Um tratamento especial é apresentado para o caso em que a variedade é um grupo de Lie munido de uma métrica Lorentziana invariante à esquerda. Mais especificamente, tratamos o caso do espaço de Damek-Ricci 4-dimensional, Riemanniano e Lorentziano. Usando a fórmula da representação de Weierstrass mostramos que existe uma única solução do problema de Björling para superfícies imersas em grupo de Lie Lorenzianos. Por fim, apresentamos alguns exemplos de superfícies mínimas construídas através do prolema de Björling para os casos em que os espaços ambientes, dotados de uma métrica Lorentziana invariante à esquerda, são o grupo de Heisenberg de dimensão três, o espaço de De Sitter e o espaço dado pelo produto do plano hiperbólico com a reta real
Abstract: In this thesis we study minimal surfaces immersed in Lorentzian manifolds. First, we develop a general version of the Weierstrass representation formula for timelike and spacelike minimal surfaces immersed in a n-dimensional Lorentzian manifold. A special treatment is presented for the case of a Lie group equipped with a left invariant Lorentzian metric. More specifically, we consider the case of the 4-dimensional Damek-Ricci space, Riemannian and Lorentzian. Applying the Weierstrass representation formula, we prove that there exists a unique solution to the Bj\"{o}rling problem for timelike surfaces immersed in a Lorenzian Lie group, when the initial curve is a timelike or spacelike curve. Finally, we present some examples of minimal surfaces constructed via Bj\"{o}rling problem for the cases in which the ambient manifolds, equipped with a left invariant Lorentzian metric, are the Heisenberg group, the De Sitter space, and the product of the hyperbolic plane and the real line
Doutorado
Matematica
Doutora em Matemática
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Shafiq, Muhammad. "Test Charge Response of a Dusty Plasma with Grain Size Distribution and Charging Dynamics." Doctoral thesis, Stockholm : Space and Plasma Physics, Royal Institute of Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4134.
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Manfio, Fernando. "Imersões isométricas em 3-variedades Lorentzianas homogêneas." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-01072008-163534/.
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Neste trabalho, provamos um teorema de imersões isométricas em variedades Lorentzianas homogêneas tridimensionais, usando a teoria de G- estruturas. Tais variedades são aquelas consideradas na classificação das 3- variedades Lorentzianas homogêneas de Dumitrescu e Zeghib. Provamos também um teorema de rigidez isométrica para hipersuperfícies em variedades semi-Riemannianas com G-estrutura infinitesimalmente homogêneas. No caso particular em que o ambiente são variedades semi-Riemannianas dadas por produto de uma forma espacial por R ou variedades Riemannianas homogêneas tridimensionais, provamos o mesmo teorema de rigidez isométrica, porém com hipóteses mais fracas.In this work we prove an isometric embedding theorem in homogeneous Lorentzian manifolds of dimension 3, that were recently classified by Dumitrescu and Zeghib in [11]. We also prove a rigidity result of isometric embeddings of hypersurfaces in semi-Riemannian manifolds endowed with an infinitesimally homogeneous G-structure. In the special case that the semi-Riemannian manifolds are produtcs of the type Q^n_cxR, or Riemannian homogeneous 3-manifolds, the result is proven under wear assumptions.
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Van, den Broeck Samuel. "Optique statistique appliquée à la granulométrie submicronique : simulation d'un signal gaussien lorentzien." Rouen, 1998. http://www.theses.fr/1998ROUES020.
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Ce travail a pour objet de simuler le signal généré par des particules lors d'une diffusion quasi élastique de la lumière. Le but est de disposer d'un outil numérique susceptible de reproduire diverses configurations expérimentales et de pouvoir évaluer de nouvelles méthodes d'analyses du signal enregistré. La simulation proposée génère les temps d'arrivée des photoélectrons issues d'un photomultiplicateur. Nous nous sommes limités ici au cas connu théoriquement d'un ensemble de particules sphériques monodispersées. Les différentes étapes du calcul sont : 1. Génération d'un signal gaussien lorentzien à partir d'un bruit blanc filtre. Ce signal simule le champ diffusé par les particules ; 2. Génération d'un processus de poisson non homogène à partir du signal gaussien lorentzien. Ce processus simule la réponse de la photocathode à l'intensité diffusée. Le nombre de points maximum généré par fichier est de 524288 (2#1#9). La validité de la simulation est testée en comparant des statistiques de premier et de deuxième ordre du champ diffusé par les particules avec leurs valeurs initiales. La densité de probabilité des intervalles de temps des photoélectrons et la fonction d'autocorrélation du nombre de photocoups sont comparées favorablement avec leurs expressions théoriques respectives.
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Escobar, Montecino Claudia Evelyn. "Classificação das hipersuperfícies lorentzianas de R1n para Rn1+1." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7189.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
In this dissertation we present a result of classi cation of isometric hypersurfaces between Lorentz-Minkowski spaces due to L. K. Graves [5], which generalizes a classic theorem of Hartman and Nirenberg [7], where hypersurfaces were classi ed among Euclidean spaces. The technique we use in this classi cation of hypersurfaces is to rst study the completeness of the relative nullity foliation, and split the demonstration in two cases depending of the foliation be degenerate or not degenerate.
Nesta dissertação apresentamos um resultado de classi cação das hipersuperfícies isométricas entre espaços de Lorentz-Minkowski devida a L. K. Graves [5], o qual generaliza um teorema clássico de Hartman e Nirenberg [7], em que foram classi cadas as hipersuperfícies isométricas entre espaços euclidianos. A técnica que usamos na classi cação dessas hipersuperfícies é estudar primeiro a completitude da folheação de nulidade relativa e dividir a demonstração em dois casos dependendo da folheação ser degenerada ou não degenerada.
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Albujer, Brotons Alma Luisa. "Geometría global de superficies espaciales en espacios producto lorentzianos." Doctoral thesis, Universidad de Murcia, 2008. http://hdl.handle.net/10803/10968.
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A lo largo de esta tesis estudiamos la geometría global de las superficies espaciales, y maximales en particular, en espacios producto lorentzianos. En primer lugar generalizamos el teorema de Calabi-Bernstein al caso de superficies maximales en un producto lorentziano. También estudiamos algunos problemas locales, que a posteriori tendrán importantes repercusiones globales. Los producto lorentzianos forman parte de la familia de los espacios de Robertson-Walker generalizados, al igual que los espacios tipo steady state. Las superficies equivalentes a las superficies maximales en un espacio tipo steady state son las superficies espaciales con H=1. En este contexto damos un resultado de unicidad para superficies espaciales completas con curvatura media constante acotadas del infinito en un espacio tipo steady state. Por último consideramos superficies espaciales con curvatura de Gauss constante en espacios producto, tanto lorentzianos como riemannianos. En este caso obtenemos algunos resultados de tipo Calabi-Bernstein cuando M es la esfera S2.Along this PhD thesis we study the global geometry of spacelike surfaces, and in particular maximal surfaces, in Lorentzian product spaces. Firstly, we generalize the Calabi-Bernstien theorem when considering maximal surfaces in a Lorentzian product. We also study some local problems, which a posteriori will have important global consequences. The Lorentzian products are part of the family of the generalized Robertson-Walker spaces. Also the steady state type spaces form a subfamily of such spaces. The equivalent surfaces to the maximal ones in a steady state type space are the spacelike surfaces with H=1. In this context, we give a uniqueness result for complete spacelike surfaces with constant mean curvature bounded from the infinity of a steady state type space. Finally, we consider spacelike surfaces with constant Gaussian curvature in Riemannian and Lorentzian product spaces. In this case, we obtain some Calabi-Bernstein type results when M is the sphere S2
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Rosa, Valeria Mattos da. "Estabilidade de curvas tipo-tempo fechadas em variedades lorentzianas." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306273.
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Orientador: Patricio Anibal Letelier SotomayorTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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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
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Schlenker, Jean-Marc. "Surfaces convexes dans des espaces lorentziens a courbure constante." Palaiseau, Ecole polytechnique, 1994. http://www.theses.fr/1994EPXX0025.
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Nous etudions les immersions isometriques de surfaces a courbures kcko dans des espaces lorentziens de dimension 3 a combine constante ko, et en particulier les degenerescences de suites de telles immersions. Nous en deduisons des resultats d'existence et d'unicite d'immersions isometriques de surfaces compactes dans l'espace de sitter, ainsi que des resultats d'existence quand les surfaces sont seulement completes. Enfin, on enonce des resultats de non existence d'immersion isometrique en dimension plus grande
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Rodriguez, Blanco Esther. "Etude des systèmes lorentziens dans le spectre des quasars." Paris 7, 2005. http://www.theses.fr/2005PA077119.
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Lorentzen, Kai [Verfasser]. "Systematische Variabilitätsreduktion zur kontinuierlichen Verbesserung von Fließlinien / Kai Lorentzen." Aachen : Shaker, 2012. http://d-nb.info/1067736077/34.
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Monclair, Daniel. "Dynamique lorentzienne et groupes de difféomorphismes du cercle." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2014. http://tel.archives-ouvertes.fr/tel-01061010.
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Cette thèse comporte deux parties, axées sur des aspects différents de la géométrie lorentzienne. La première partie porte sur les groupes d'isométries de surfaces lorentziennes globalement hyperboliques spatialement compactes, particulièrement lorsque le groupe exhibe une dynamique non triviale (action non propre). Le groupe d'isométries agit naturellement sur le cercle par difféomorphismes, et les résultats principaux portent sur la classification de ces représentations. Sous une hypothèse sur le bord conforme, on obtient une conjugaison par homéomorphisme avec l'action projective d'un sous-groupe de PSL(2,R) ou de l'un de ses revêtements finis. La différentiabilité de la conjuguante est étudiée, avec des résultats qui garantissent une conjugaison dans le groupe de difféomorphismes du cercle dans certains cas. On donne également des contre-exemples à l'existence d'une conjugaison différentiable, y compris pour des groupes ayant une dynamique riche. Ces constructions s'appuient sur l'étude de flots hyperboliques en dimension trois. Sans l'hypothèse sur le bord conforme, on obtient une semi conjugaison et un isomorphisme de groupes. On construit également des exemples pour lesquels il n'existe pas de conjugaison topologique. La seconde partie de cette thèse étudie un espace-temps vu comme un système dynamique multi-valuée : à un point on associe sont futur causal. Cette approche, déjà présente dans les travaux de Fathi et Siconolfi, permet de concrétiser le lien entre fonctions de Lyapunov en systèmes dynamiques et fonctions temps. Le résultat principal est une version lorentzienne du Théorème de Conley : on peut définir l'ensemble récurrent par chaînes d'un espace-temps, et il existe une fonction continue croissante le long de toute courbe causale orientée vers le futur, strictement croissante si le point de départ de la courbe n'est pas dans l'ensemble récurrent par chaînes. Ces techniques s'adaptent aussi dans un espace-temps stablement causal, ce qui permet de donner une nouvelle preuve d'une partie du Théorème d'Hawking.
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Noterdaeme, Pasquier. "Systèmes Lorentziens Lyman-alpha à grand décalage spectral: Etude de l'hydrogène moléculaire." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2008. http://tel.archives-ouvertes.fr/tel-00414784.
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Les systèmes Lorentziens Lyman-alpha à grand décalage spectral, observés en absorption sur la ligne de visée de quasars, sont les signatures spectrales du milieu interstellaire dans l'Univers lointain. Peu d'outils sont cependant à notre disposition pour comprendre les propriétés physiques des objets associés. Une technique qui se base sur de la physique bien comprise et qui a été largement appliquée au milieu interstellaire local est l'étude de l'hydrogène moléculaire. Les propriétés radiatives et collisionnelles spécifiques de cette molécule en font une sonde très sensible aux conditions physiques du gaz.Dans cette thèse, j'étudie la présence d'hydrogène moléculaire dans le milieu interstellaire à grand décalage spectral en m'appuyant sur un échantillon unique de systèmes Lorentziens Lyman-alpha observés à grand rapport signal-à-bruit et haute résolution spectrale. Je présente des travaux dont l'objectif est de comprendre les propriétés et les conditions physiques du gaz neutre associé à ces systèmes (température, densité, composition chimique, fraction moléculaire, contenu en poussières, intensité du champ de radiation incident).
J'effectue en parallèle une recherche systématique et une étude statistique des systèmes Lorentziens afin de mesurer le contenu en gaz neutre de l'Univers, caractériser sa distribution et son évolution au cours du temps et contraindre ainsi la formation des galaxies.
Je montre enfin la possibilité de détecter et d'étudier d'autres molécules telles que l'hydrogène moléculaire deutéré et le monoxyde de carbone dans le milieu interstellaire à grand décalage spectral. Les outils d'analyse automatique de spectres développés dans cette thèse ont conduit à la première détection de CO dans un tel milieu, ouvrant la voie à l'astrochimie du milieu interstellaire dans l'Univers lointain.
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Noterdaeme, Pasquier. "Systèmes Lorentziens Lyman-α à grand décalage spectral : étude de l'hydrogène moléculaire." Paris 6, 2008. https://tel.archives-ouvertes.fr/tel-00414784.
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Belraouti, Mehdi. "Convergence asymptotique des niveaux de temps quasi-concaves dans un espace temps à courbure constante." Phd thesis, Université d'Avignon, 2013. http://tel.archives-ouvertes.fr/tel-00978618.
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Dans cette thèse, nous nous intéressons aux espaces temps dit globalement hyperboliques Cauchy compacts. Ce sont des espaces temps qui admettent une fonction, dite fonction temps de Cauchy, propre qui croit strictement le long des courbes causales inextensibles. Les niveaux de telles fonctions sont des hypersurfaces de type espace appelées hypersurfaces de Cauchy. La donnée d'une fonction temps définit naturellement une famille à 1-paramètres d'espaces métriques. Notre but est d'étudier le comportement asymptomatique de ces familles d'espaces métriques Il y a deux cas de figure à considérer : le premier étant le comportement asymptomatique dans le passé ; le deuxième est celui du comportement asymptomatique dans le futur. Plus de conditions géométriques sur l'espace temps et les fonctions temps à considérer seront nécessaires