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Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24403号 / 理博第4902号 / 新制||理||1700(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 高柳 匡, 教授 杉本 茂樹, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis is about thwo papers related to extra dimensions. Paper A discusses extrinsic curvature effects, and paper B treats symmetries of supersymmetric membranes. In the part of this thesis related to paper A, we extend the theory of non-relativistic quantum particles confined to submanifolds to relativistic boson fields. We show that a Klein-Gordon field constrained to a submanifold of a Lorentzian manifold experiences an induced potential similar to the one for the Schr{\"o}dinger equation. We embedd the Schwarzschild solution and the Robertson-Walker space-time and derive the induced potentials. Possible physical consequences of these induced potentials are also discussed. The second part is related to paper B, we study the dynamics of supersymmetric membranes, which are higher dimensional generalizations of supersymmetric strings. We derive a supersymmetric analogue of a dynamical symmetry for bosonic membranes. / QC 20110427

In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given <i>n</i>-dimensional spacetime within an (<i>n</i>+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard <i>n</i>-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a <i>d</i>-brane that takes the form of a thin shell encircling a (<i>d</i>+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.

In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given <i>n</i>-dimensional spacetime within an (<i>n</i>+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard <i>n</i>-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a <i>d</i>-brane that takes the form of a thin shell encircling a (<i>d</i>+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2017-07-05T11:27:51Z No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-08T15:19:39Z (GMT) No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) / Made available in DSpace on 2017-08-08T15:19:39Z (GMT). No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) Previous issue date: 2013-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho vamos mostrar que o sistema chamado de “mundo brana” para representar o nosso Universo, introduzido por Randall-Sundrum (RS) no fim dos anos noventa, pode ser na verdade representado por branas curvas no espaço de de Sitter e Anti-de Sitter. Originalmente o sistema RS representaria um Universo com cinco dimensões onde o modelo padrão ficaria confinado em uma brana e os grávitons ficariam confinados na outra brana. Este sistema foi construído com uma métrica de Minkowski “torcida” com cinco dimensões onde os grávitons, responsáveis pelo campo gravitacional no modelo padrão, se deslocariam através da quinta dimensão, que por sua vez é infinita. E a ação padrão da relatividade geral, a ação de Einstein-Hilbert, foi a utilizada por RS. Neste trabalho de dissertação de mestrado vamos adotar uma ação modificada usada atualmente para explicar efeitos cosmológicos como a energia escura e a expansão do Universo por exemplo, ou seja, a ação com uma gravitação modificada chamada de f(R). Aqui vamos usar uma f(R) totalmente generalizada e suas consequências cosmológicas e viabilidade serão analisadas. Finalmente, vamos demonstrar que as partículas do modelo padrão estão confinadas nesta brana curva. Os resultados obtidos aqui generalizam totalmente outros resultados obtidos na literatura atual sobre mundo brana com branas grossas e são por isso, originais e serão submetidos à publicação. / In this work we will show that the so-called “brane world” framework introduced by Randall-Sundrum (RS), to represent our Universe, at the late nineties can be represented in fact by bent branes in de Sitter and Anti-de Sitter space with a generalized model for gravity. At the beginning, the RS scenario represent a Universe in five dimensions where the Standard Model is confined in one brane and the gravitons were confined in the another one. This model was build with a warped Minkowski metric with five dimensions where the gravitons, which are responsible by the gravitational field, are able to move through the fifth dimension, which is infinity. The standard general relativity action, namely, the Einstein-Hilbert action, was the one used by RS. In this Master dissertation we will adopt a modified action used at present to explain some cosmological effects like dark energy and Universe expansion, for example, i.e., we will use an action with a modified gravitation called f(R). However, here we will use a generalized f(R) and their cosmological consequences and viability will be analyzed. Finally, we will show that the particles of the Standard Model are confined at this bent brane. The results obtained here generalize altogether the others results obtained in the current literature concerning braneworlds with thick branes and are, consequently, new ones, which will be published elsewhere.