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In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, de

The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1

Monocentric lenses provide compact, broadband, high resolution, wide-field imaging. However, they produce a curved image surface and have found limited use. The use of an appropriately machined fiber bundle to relay the curved image plane onto a flat focal plane array (FPA) has recently emerged as a potential solution. Unfortunately the spatial sampling that is intrinsic to the fiber bundle relay can have a negative effect on image resolution, and vignetting has been identified as another potential shortcoming of this solution. This thesis describes a metamaterial lens yielding a high-performance image relay from a curved surface to a flat focal plane. Using quasi-conformal transformation optics, a Maxwell's fish-eye lens is transformed into a concave-plano shape. A design with a narrower range of constitutive parameters is deemed more likely to be manufacturable. Therefore, the way in which the particular shape of the concave-plano reimager influences the range of needed constitutive parameters is explored. Finally, image quality metrics, such as spot size and light efficiency, are quantified.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20656号 / 理博第4321号 / 新制||理||1621(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this project a recent model of inflation in which the Standard Model Higgs field with a nonminimal coupling to gravity takes on the role of the inflaton field is investigated. The tensor to scalar ratio, spectral index and the running of the spectral index  is calculated for a tree level analysis and compared with the Planck experiment. The value of the nonminimal coupling constant $\xi$ is estimated by obtaining a relation between the amplitude of scalar perturbations and the Higgs mass, it is found that $\xi \sim 10^4$. The basic aspects of how the results are modified through quantum corrections and what the consequences of the nonminimal coupling are for the effective field theory description is discussed. It is found that a tree level analysis yields predictions which are inside the allowed regions of the cosmological parameters given by the Planck experiment. The large value of the nonminimal coupling leads to unitarity problems for this model of inflation.  However quantum effects will have a significant effect and how they modify the results of the tree level analysis is what decides if Higgs inflation is a viable theory. / I detta projekt undersöker vi en modell av kosmisk inflation där Higgsfältet med en ickeminimal koppling till tyngdkraften är mekanismen bakom inflation. Vi utför en klassisk analys och beräknar modellens föresägelser för ett antal kosmologiska parametrar som jämförs med Planck experimentet. Vi uppskattar värdet på den ickeminimala kopplingen $\xi$ och finner att $\xi \sim 10^4$. De grundläggande aspekterna bakom kvantanalysen samt vad effekten av den ickeminimala kopplingen har på beskrivningen i termer av en effektiv fältteori diskuteras. Vi finner att en klassisk analys ger förutsägelser som passar väl med Planckexperimentet men att den ickeminimala kopplingen leder till unitaritetsproblem för denna modell av inflation. Kvanteffekter kan dock ha en avsevärd effekt på resultat och en utförlig analys som tar dem till hänsyn krävs för att avgöra om Higgsinflation är en möjlig modell för inflation.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-26T18:18:25Z No. of bitstreams: 1 monalisasilvadeoliveira.pdf: 473060 bytes, checksum: 1e394ef35b65c023c130f0dbca9a9d12 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-13T12:04:23Z (GMT) No. of bitstreams: 1 monalisasilvadeoliveira.pdf: 473060 bytes, checksum: 1e394ef35b65c023c130f0dbca9a9d12 (MD5) / Made available in DSpace on 2017-05-13T12:04:23Z (GMT). No. of bitstreams: 1 monalisasilvadeoliveira.pdf: 473060 bytes, checksum: 1e394ef35b65c023c130f0dbca9a9d12 (MD5) Previous issue date: 2013-02-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, fazemos uma pequena revisão sobre tensores e sua utilização na Relatividade Geral, apresentamos o método de transformação conforme e o teorema da fatorização e discutimos as soluções de Schwarzschild com e sem constante cosmológica. Então, a solução de Schwarzschild com constante cosmológica é derivada, a partir das equações de campo de Einstein, utilizando-se os conceitos abordados. / In this work, we make a brief review of tensors and their use in General Relativity, we present the local conformal transformation method and the factorization theorem and we discuss Schwarzschild's solutions with and without cosmological constant. Then, the Schwarzschild's solution with cosmological constant is derived, from the Einstein's field equations, using the concepts addressed.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-09T17:37:21Z No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-29T12:08:53Z (GMT) No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) / Made available in DSpace on 2017-06-29T12:08:53Z (GMT). No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) Previous issue date: 2015-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Teorias com derivadas de alta ordem e sua invariância sob transformações conformes são ferramentas poderosas em Teoria Quântica de Campos em espaços curvos. O principal propósito de nosso estudo é trabalhar no sentido de obter uma generalização do operador quadridimensional conforme de Paneitz para um operador análogo em seis dimensões (∆6). A consecução de um operador conformalmente invariante contendo seis derivadas justifica a escolha de se trabalhar nesta dimensão como um recurso mais simples para sua obtenção. Tal operador seria de fundamental importância na integração da anomalia conforme em teorias com derivadas de sexta ordem. A forte relação entre operadores conformes e a densidade de Euler foi investigada em D = 2 e D = 4. O termo da densidade de Euler - o qual é conhecido em 4D como termo topológico de Gauss-Bonnet - foi estendido a seis dimensões. Em dimensões pares, tal termo é representado por potências de D/2 de contrações dos tensores de Riemann e Ricci, cada um dos quais contendo D derivadas. A transformação dos escalares de terceira ordem na curvatura os quais aparecem no estudo da anomalia conforme e da densidade de Euler em seis dimensões foi obtida como um primeiro passo rumo ao nosso objetivo de obter ∆6. / Higher-derivative theories and their invariance under conformal transformati ons are powerful tools in Quantum Field Theory in curved spaces. The main purpose of our study is to work towards achievement of a generalization of the four dimensional Paneitz conformal operator to analogous six dimension one (∆6). Achieving a six deri vative conformally invariant operator justifies the choice of working in such dimension as a simpler resource for obtaining it. This operator would be of fundamental account in the integration of the conformal anomaly in sixth order derivatives theories. The strong relation between conformal operators and Euler density has been investigated in D = 2 e D = 4. Euler density term - which 4D version is known as topological Gauss-Bonnet term - was extended to the six dimension. In even dimensions, it is represented by D/2 powers of contracted Riemann and Ricci tensors, each of them carrying D derivatives. The transformation of the third order curvature scalars that arise in the study of the conformal anomaly and Euler density in six dimension was obtained as a first step to our goal of achieving ∆6.