In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. <br /><br /> Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden <em>SL</em>(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the <em>C</em>-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalizing the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalizations of Kaluza-Klein magnetic monopoles, generalizing the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalizing the known Reissner-Nordström solutions.

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. <br /><br /> Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden <em>SL</em>(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the <em>C</em>-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalizing the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalizations of Kaluza-Klein magnetic monopoles, generalizing the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalizing the known Reissner-Nordström solutions.

Einstein's field equations are extremely difficult to solve, and when solved, the solutions are even harder to understand. In this thesis, two analysis tools are developed to explore and visualize the curvature of spacetimes. The first tool is based on a thorough examination of observer independent curvature invariants constructed from different contractions of the Riemann curvature tensor. These invariants are analyzed through their gradient fields, and attention is given to the resulting flow and critical points. Furthermore, we propose a Newtonian analog to some general relativistic invariants based on the underlying physical meaning of these invariants, where they represent the cumulative tidal and frame-dragging effects of the spacetime. This provides us with a novel and intuitive tool to compare Newtonian gravitational fields to exact solutions of Einstein's field equations on equal footing. We analyze the obscure Curzon-Chazy solution using the new approach, and reveal rich structure that resembles the Newtonian gravitational field of a non-rotating ring, as it has been suspected for decades. Next, we examine the important Kerr solution, which describes the gravitational field of rotating black holes. We discover that the observable part of the geometry outside the black hole's event horizon depends significantly on its angular momentum. The fields representing the cumulative tidal and frame-dragging forces change qualitatively at seven specific values of the dimensionless spin parameter of the black hole. The second tool we develop in this thesis is the accurate construction of the Penrose conformal diagrams. These diagrams are a valuable tool to explore the causal structure of spacetimes, where the entire spacetime is compactified to a finite size, and the coordinate choice is fixed such that light rays are straight lines on the diagram. However, for most spacetimes these diagrams can only be constructed as a qualitative guess, since their null geodesics cannot be solved. We developed an algorithm to construct very accurate Penrose diagrams based on numeric solutions to the null geodesics, and applied it to the McVittie metric. These diagrams confirmed the long held suspicion that this spacetime does indeed describe a black hole embedded in an isotropic universe. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-30 14:02:55.865

Graphene has recently become the focus of enormous attention for experimentalists and theorists alike mainly due to its unique electronic properties. However, the limited way in which one can control these properties is a major obstacle for device applications. The unifying theme of this thesis is to propose and thoroughly justify ways to control the electronic properties of graphene and carbon nanotubes by light or static electric and magnetic fields and to harness these properties for optoelectronic applications. A linearly polarized excitation is shown to create a strongly anisotropic distribution of photoexcited carriers in graphene, where the momenta of photoexcited carriers are aligned preferentially normal to the polarization plane. This effect offers an experimental tool to generate highly directional photoexcited carriers which could assist in the investigation of "direction-dependent phenomena" in graphene-based nanostructures. The depolarization of hot photoluminescence is used to study relaxation processes in graphene, both free standing and grown on silicon carbide. This analysis is extended to include the effect of a magnetic field, thereby allowing one to obtain the momentum relaxation times of hot electrons. The analysis of momentum alignment in the high frequency regime shows that a linearly polarized excitation allows the spatial separation of carriers belonging to different valleys. Quasi-metallic carbon nanotubes are considered for terahertz applications. They are shown to emit terahertz radiation when a potential difference is applied across their ends and their spontaneous emission spectra have a universal frequency and bias voltage dependence. It is shown that the same intrinsic curvature which opens the gap in the quasi-metallic carbon nanotube energy spectrum also allows optical transitions in the terahertz range. The exciton binding energy in narrow-gap carbon nanotubes is calculated and found to scale with the band gap and vanishes as the gap decreases, even in the case of strong electron-hole attraction. Therefore, excitonic effects should not dominate in narrow-gap nanotubes. Contrary to widespread belief, it is shown that full confinement is possible for zero-energy states in pristine graphene. The exact analytical solutions for the zero-energy modes confined within a smooth one-dimensional potential V = α/ cosh (βx) are presented. This potential provides a good fit for the potential profiles of top-gated graphene structures. It is shown that there is a threshold value of the characteristic potential strength α/β for which the first mode appears, in striking contrast to the non-relativistic case. A relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.

Orientador: José Francisco Gomes / Banca: Galen Mihaylov Sotkov / Banca: Abraham Hirsz Zimerman / Banca: Paulo Teotônio Sobrinho / Banca: Márcio José Martins / Resumo: Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do modelo WZNW mediante a calibração da ação Swznw e corresponde ao primeiro membro de grau negativo q = -1 de uma hierarquia de modelos cKP do tipo dyon. O modelo mais simples não relativístico dentro desta hierarquia corresponde ao grau q = 2 positivo. As soluções de 1-sóliton para ambos modelos foram construídas e relações explícitas entre ambas soluções (assim como entre as cargas conservadas) foram encontradas. Outro modelo integrável com simetrias não abelianas locais SL(2) X U(1) é introduzido. Numa aproximação à integrabilidade em espaços não-comutativos estudamos generalizações não comutativas no plano dos modelos integráveis bidimensionais sine-, sinh-Gordon e U(N) Quiral Principal. Calculando a amplitude de espalhamento à nível de árvore de um processo de produção de partículas provamos que a versão não-comutativa do modelo de sinh-Gordon que se obtém mediante a deformação Moyal da respectiva ação não é integrável. Por outro lado, a incorporação de vínculos adicionais que são obtidos a partir da generalização da condição de curvatura nula, tornam o modelo integrável. O modelo Quiral Principal generalizado a partir da deformação Moyal da ação, preserva a sua integrabilidade, ao contrário dos modelos sinh-Gordon e sine-Gordon. / Abstract: In this thesis we have constructed and studied a new class of two-dimensional integrable models (relativistic and nonrelativistic), related to the affine algebra 'A IND.3 POT.(1)'. These models admit U(1) X U(1) charged topological solitons. The affine Toda relativistic model is constructed from the gauged WZNW action and corresponds to the first negative grade q = -1 member of a dyonic hierarchy of cKP models. The simplest nonrelativistic model corresponds to the positive grade q = 2 of this hierarchy. The 1-soliton solutions for both models were constructed and explicit relations between them (and the conserved charges as well) were found. Another integrable model with local nonabelian SL(2) X U(1) simetries is introduced. In the context of integrability on noncommutative spaces, we have studied noncommutative generalizations on the plane of the two-dimensional integrable models sine-, sinh-Gordon and U(N) Principal Quiral. By computing for the sinh-Gordon model, the tree-level amplitude of a process of production of particles, we proved that the noncommutative generalization of this model that it is obtained by the Moyal deformation of the corresponding action is not integrable. On the other hand, the addition of extra constraints, obtained by the generalization of the zero-curvature method, renders the integrability of the model. The generalization of the Principal Quiral model by the Moyal deformation of the action preserves the integrability, contrary to the previous case / Doutor

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02Bitstream added on 2014-06-13T20:23:07Z : No. of bitstreams: 1 cabreracarnero_i_dr_ift.pdf: 1015322 bytes, checksum: 915c6683e6c1c022f54ca1d9f5a03904 (MD5) / Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do modelo WZNW mediante a calibração da ação Swznw e corresponde ao primeiro membro de grau negativo q = -1 de uma hierarquia de modelos cKP do tipo dyon. O modelo mais simples não relativístico dentro desta hierarquia corresponde ao grau q = 2 positivo. As soluções de 1-sóliton para ambos modelos foram construídas e relações explícitas entre ambas soluções (assim como entre as cargas conservadas) foram encontradas. Outro modelo integrável com simetrias não abelianas locais SL(2) X U(1) é introduzido. Numa aproximação à integrabilidade em espaços não-comutativos estudamos generalizações não comutativas no plano dos modelos integráveis bidimensionais sine-, sinh-Gordon e U(N) Quiral Principal. Calculando a amplitude de espalhamento à nível de árvore de um processo de produção de partículas provamos que a versão não-comutativa do modelo de sinh-Gordon que se obtém mediante a deformação Moyal da respectiva ação não é integrável. Por outro lado, a incorporação de vínculos adicionais que são obtidos a partir da generalização da condição de curvatura nula, tornam o modelo integrável. O modelo Quiral Principal generalizado a partir da deformação Moyal da ação, preserva a sua integrabilidade, ao contrário dos modelos sinh-Gordon e sine-Gordon. / In this thesis we have constructed and studied a new class of two-dimensional integrable models (relativistic and nonrelativistic), related to the affine algebra 'A IND.3 POT.(1)'. These models admit U(1) X U(1) charged topological solitons. The affine Toda relativistic model is constructed from the gauged WZNW action and corresponds to the first negative grade q = -1 member of a dyonic hierarchy of cKP models. The simplest nonrelativistic model corresponds to the positive grade q = 2 of this hierarchy. The 1-soliton solutions for both models were constructed and explicit relations between them (and the conserved charges as well) were found. Another integrable model with local nonabelian SL(2) X U(1) simetries is introduced. In the context of integrability on noncommutative spaces, we have studied noncommutative generalizations on the plane of the two-dimensional integrable models sine-, sinh-Gordon and U(N) Principal Quiral. By computing for the sinh-Gordon model, the tree-level amplitude of a process of production of particles, we proved that the noncommutative generalization of this model that it is obtained by the Moyal deformation of the corresponding action is not integrable. On the other hand, the addition of extra constraints, obtained by the generalization of the zero-curvature method, renders the integrability of the model. The generalization of the Principal Quiral model by the Moyal deformation of the action preserves the integrability, contrary to the previous case

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-06T00:06:09Z (GMT). No. of bitstreams: 1 Vogt_Daniel_D.pdf: 2048895 bytes, checksum: d7173036404048baab332998c8c336cc (MD5) Previous issue date: 2006 / Resumo: Soluções exatas das equações do campo de Einstein que representam espaços-tempo com distribuições de matéria em forma de discos são construídas pelo método inverso (método das imagens). Estas soluções incluem discos estáticos ínos de fluido perfeito com e sem halos, discos estáticos finos de fluido perfeito com carga elétrica e modelos de discos finos formados por poeira carregada. São estudadas ainda novas soluções em vários sistemas de coordenadas que representam discos estáticos grossos com espessura constante. Uma forma particular para a métrica isotrópica em coordenadas cilíndricas é usada para obter-se versões relativísticas de pares potencial-densidade Newtonianos comumente usados na Astronomia Galáctica. Um modelo relativístico simplificado, porém exato, de um núcleo ativo de galáxia também é apresentado. Finalmente, é feito um estudo de alguns pares-potencial densidade Newtonianos obtidos a partir da expansão multipolar do potencial Newtoniano que generalizam pares conhecidos / Abstract: Exact solutions of Einstein field equations that represent space-times with disklike matter distributions are constructed using the inverse method (image method). These solutions include static thin perfect uid disks with and without halos, static thin charged perfect uid disks and models of thin charged dust disks. New solutions in various coordinate systems that represent static thick disks with constant thickness are also studied. A particular form of the isotropic metric in cylindrical coordinates is employed to obtain relativistic versions of Newtonian potential-density pairs commonly used in Galactic Astronomy. A simplified, although exact, relativistic model of an active galactic nuclei is also presented. Finally, some Newtonian potential-density pairs obtained from the Newtonian multipolar expansion that generalize known pairs are studied. / Doutorado / Física / Doutor em Ciências

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17871号 / 工博第3780号 / 新制||工||1578(附属図書館) / 30691 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 谷口 栄一, 教授 藤井 聡, 准教授 宇野 伸宏 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19481号 / 理博第4141号 / 新制||理||1595(附属図書館) / 32517 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 藤 定義, 教授 佐々 真一, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

O presente trabalho se destina a um estudo detalhado da chamada equação de spin, a qual pode ser utilizada para descrever o comportamento de sistemas de dois níveis. Para campos externos dados por funções reais, esta equação pode ser identificada com uma redução da equação de Pauli para o caso 0+1 dimensional. Inicialmente, demonstraremos a relação entre esta equação de spin e várias outras equações relacionadas com diversos problemas em física. Com estas relações, podemos construir novas soluções da equação de spin a partir do conhecimento de soluções exatas destes outros problemas e, por outro lado, estender a aplicação das soluções obtidas. Em seguida, descrevemos a forma geral da solução desta equação, construímos o operador de evolução e resolvemos o problema inverso, i.e., a determinação do campo externo supondo o conhecimento de uma solução. Finalizando, para o importante caso de campos externos reais, desenvolvemos um método de construção de novas soluções a partir de uma solução previamente conhecida, utilizando a chamada transformação de Darboux. Em particular, demonstramos a existência de operadores de entrelaçamento de Darboux, que não violam a estrutura específica dos sistemas de dois níveis, e permitem construir novos campos externos também dados por funções reais. Como resultado destes desenvolvimentos, apresentamos uma série de novas soluções exatas para a equação de spin. / The aim of the present work is to study in detail the so called spin equation, which can be used to describe the behavior of two-level systems. We recall that, for real external fields, this equation can be treated as a reduction of the Pauli equation to the 0+1 dimensional base. Initially, we present the relation between the spin equation and some other equations related to diferent physical problems. With these relations, we construct new solutions to the spin equation from the knowledge of the exact solutions of these other problems and, on the other hand, extend the applicability of the obtained solutions. After that, we describe the general solution of the spin equation, construct the evolution operator and solve the inverse problem, i.e., the construction of the external field from a given supposed solution. Finally, for the important case of real fields, we develop a method to construct new solutions from a previously known one, by the application of the so called Darboux transformation. In particular, we demonstrate the existence of Darboux intertwining operators which do not violate the specific structure of the two-level systems and allow the construction of external fields which are also given by real functions. As a result of all these developments, we present several new sets of exact solutions for the spin equation.