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.

This is a thesis which contributes to research in two different fields: theoretical physics and physics education research. The common link between these two research areas is that both involve explorations of abstract physics and mathematical representations, but from different perspectives. The first part of this thesis is situated in theoretical physics. Here a cosmological scenario is explored where a de Sitter phase is replaced with a phase described with a scale factor a(t) ~ tq, where 1/3<1. This scenario could be viewed as an inflationary toy model, and is shown to open up the possibility of an information paradox. This potential paradox is resolved even in the worst case scenario by showing that the time scales involved for such a paradox to occur is of the order of magnitude of the recurrence time for the de Sitter space. The second part of this thesis is situated in physics education research. A number of learning situations that are experienced as abstract by students are explored: probability in one dimensional quantum tunnelling; the mindsets that students adopt towards understanding physics equations used in typical teaching scenarios; and what students focus on when presented with physics equations. The results for the quantum scattering study are four phenomenographic categories of description, for the mind sets study, six epistemological components of mindsets and for the focus on physics equations study, three foci creating five levels of increasing complexity of ways of experiencing physics equations.  Pedagogical implications of these results are discussed.

Kaluza-Klein theories generally in $(4+D)$ and more specifically in five dimensions are reviewed. The magnetic monopole solutions found in the Kaluza-Klein theories are generally reviewed and their generalizations to Anti-de Sitter spacetimes are discussed.

Nous étudions différentes situations de distribution de la matière d’une bulle de masse négative. En effet, pour les bulles statiques et à symétrie sphérique, nous commençons par l’hypothèse qui dit que cette bulle, étant une solution des équations d’Einstein, est une déformation au niveau d’un champ scalaire. Nous montrons que cette idée est à rejeter et à remplacer par celle qui dit que la bulle est formée d’un fluide parfait. Nous réussissons à démontrer que ceci est la bonne distribution de matière dans une géométrie Schwarzschild-de Sitter, qu’elle satisfait toutes les conditions et que nous sommes capables de résoudre numériquement ses paramètres de pression et de densité. / We study different situations of matter distribution of a negative mass bubble. For the case of static and spherically symmetric bubbles, we start with the hypothesis saying that this kind of bubble, being a solution of Einstein equations, is a deformation of scalar field. We show that this idea must be rejected and replaced by another saying that the bubble is formed by a perfect fluid. We succeed to demonstrate that this is the proper matter distribution within Schwarzschild-De Sitter geometry, that it satisfies all conditions and that we’re capable of resolving numerically its parameters of pressure and density.

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.

No description available.

Submitted by Johan Renzo Salazar Malpartida (johanrenzosm@gmail.com) on 2018-09-24T18:20:35Z No. of bitstreams: 1 0-Thesis.pdf: 349725 bytes, checksum: a61b999c76db9b574769428cae02bc08 (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: - Passar na biblioteca para elaborar a ficha catalográfica que deverá ser inserida na dissertação antes de inserir no repositório. A ficha deve consta no PDF - Corrigir o título, pois no pdf o título está em inglês. Portanto, o campo título deve ser preenchido em inglês e o campo titulo alternativo em português - entrada do seu nome deve ser pelo sobrenome do seu pai. - Se o sobrenome do seu pai for Malpartida --> deve ser preenchido Malpartida, Johan Renzo Salazar - Se o sobrenome do seu pai for Salazar --> deve ser preenchido Salazar Malpartida, Johan Renzo - Faltou inserir o abstract - Faltou preencher o campo área de concentração - Faltou preencher o campo Linha de pesquisa on 2018-09-25T17:29:41Z (GMT) / Submitted by Johan Renzo Salazar Malpartida (johanrenzosm@gmail.com) on 2018-09-26T13:20:52Z No. of bitstreams: 2 ficha catalográfica -Johan Renzo Salazar malpartida (1).pdf: 84996 bytes, checksum: 67952920d1945336e50e78b9a7752d7d (MD5) 0-Thesis.pdf: 440560 bytes, checksum: b830fa43b5d20651d6f0b7a1cd7998c9 (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Johan, Conforme orientação que foi dada ontem, a ficha catalográfica precisa ser inserida no pdf da dissertação, logo após a folha de rosto, onde consta o titulo, seu nome, orientador... on 2018-09-26T14:44:32Z (GMT) / Submitted by Johan Renzo Salazar Malpartida (johanrenzosm@gmail.com) on 2018-09-26T15:50:22Z No. of bitstreams: 3 ficha catalográfica -Johan Renzo Salazar malpartida (1).pdf: 84996 bytes, checksum: 67952920d1945336e50e78b9a7752d7d (MD5) 0-Thesis.pdf: 440560 bytes, checksum: b830fa43b5d20651d6f0b7a1cd7998c9 (MD5) 0-Thesis.pdf: 471654 bytes, checksum: 992ba3db7e6190e79618954b961abc5e (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Johan, Por favor, a ficha precisa ser anexada do jeito que foi enviada. A mesma ficou desconfigurada no pdf. Ela tem que ficar centralizada na parte inferior da página, do jeito que foi enviada Favor deletar os arquivos antigo e manter um único arquivo on 2018-09-26T18:16:10Z (GMT) / Submitted by Johan Renzo Salazar Malpartida (johanrenzosm@gmail.com) on 2018-09-26T18:37:13Z No. of bitstreams: 1 0-Thesis-merged.pdf: 573271 bytes, checksum: 37b052e0c5e3b1c119f1f920c0d3eaaa (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-09-27T17:57:19Z (GMT) No. of bitstreams: 1 salazarmalpartida_jr_me_ift.pdf: 573271 bytes, checksum: 37b052e0c5e3b1c119f1f920c0d3eaaa (MD5) / Made available in DSpace on 2018-09-27T17:57:19Z (GMT). No. of bitstreams: 1 salazarmalpartida_jr_me_ift.pdf: 573271 bytes, checksum: 37b052e0c5e3b1c119f1f920c0d3eaaa (MD5) Previous issue date: 2018-08-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Como é bem conhecido, a relatividade especial de Einstein, cuja cinemática é governada pelo grupo de Poincaré, deixa de valer na escala de Planck devido à existência de uma escala de comprimento invariante, dada pelo comprimento de Planck. Por essa razão, ela é incapaz de descrever a cinemática naquela escala. Uma solução possível para esse problema, a qual preserva a simetria de Lorentz — e consequentemente a causalidade — é substituir a relatividade especial de Einstein por uma relatividade especial na qual a cinemática é governada pelo grupo de de Sitter. Claro que uma mudança na relatividade especial irá pruduzir mudanças concomitantes na relatividade geral, a qual se torna o que chamamos de relatividade geral modificada por de Sitter. Trabalhando no contexto dessa teoria, o objetivo desse trabalho é deduzir a fórmula geral da aceleração relativa entre duas geodésicas próximas, a qual leva à equação do desvio geodésico modificada por de Sitter. Uma análise simples dos efeitos adicionais induzidos pela cinemática local de de Sitter é apresentada. / As is well-known, the Poincaré invariant Einstein special relativity breaks down at the Planck scale due to the presence of an invariant length, given by the Planck length. For this reason, it is unable to describe the spacetime kinematics at that scale. A possible solution to this problem that preserves Lorentz symmetry — and consequently causality — is arguably to replace the Poincaré invariant Einstein special relativity by a de Sitter invariant special relativity. Of course, a change in special relativity produces concomitant changes in general relativity, which becomes what we have called de Sitter modified general relativity. By working in the context of this theory, the purpose of this work is to deduce the general relative acceleration between nearby geodesics, which leads to the de Sitter modified geodesic deviation equation. A simple analysis of the additional effects induced by the local de Sitter kinematics is presented. / 33015015001P7

abstract: In the past decade, real-world applications of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAV) have increased significantly. There has been growing interest in one of these types of UAVs, called a tail-sitter UAV, due to its VTOL and cruise capabilities. This thesis presents the fabrication of a spherical tail-sitter UAV and derives a nonlinear mathematical model of its dynamics. The singularity in the attitude kinematics of the vehicle is avoided using Modified Rodrigues Parameters (MRP). The model parameters of the fabricated vehicle are calculated using the bifilar pendulum method, a motor stand, and ANSYS simulation software. Then the trim conditions at hover are calculated for the nonlinear model, and the rotational dynamics of the model are linearized around the equilibrium state with the calculated trim conditions. Robust controllers are designed to stabilize the UAV in hover using the H2 control and H-infinity control methodologies. For H2 control design, Linear Quadratic Gaussian (LQG) control is used. For the H infinity control design, Linear Matrix Inequalities (LMI) with frequency-dependent weights are derived and solved using the MATLAB toolbox YALMIP. In addition, a nonlinear controller is designed using the Sum-of-Squares (SOS) method to implement large-angle maneuvers for transitions between horizontal flight and vertical flight. Finally, the linear controllers are implemented in the fabricated spherical tail-sitter UAV for experimental validation. The performance trade-offs and the response of the UAV with the linear and nonlinear controllers are discussed in detail. / Dissertation/Thesis / Masters Thesis Aerospace Engineering 2018

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.

Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons par présenter la problématique générale et discutons notamment du rapport entre la complétude géodésique de ces variétés et une autre notion de complétude propre aux (G,X)-structures. Nous donnons également dans le chapitre 1 une nouvelle preuve d’un théorème de Bromberg et Medina qui classifie les métriques lorentziennes invariantes à gauche sur SL(2,R) dont le flot géodésique est complet. Conjecturalement, toute (G,X)-structure pseudo-riemannienne sur une variété compacte est complète. Nous prouvons ici que cela est vrai pour certaines géométries, sous l’hypothèse que la (G,X)-structure est a priori kleinienne. On en déduit que, pour ces géométries, la complétude est une condition fermée. Lorsque X est un groupe de Lie de rang 1 muni de sa métrique de Killing, ce résultat complète un théorème de Guéritaud–Guichard–Kassel–Wienhard selon lequel la complétude est une condition ouverte. Nous nous tournons ensuite vers l’étude des représentations d’un groupe de surface à valeurs dans les isométries d’une variété riemannienne M complète simplement connexe de courbure sectionnelle inférieure à -1. Étant donnée une telle représentation ρ, nous montrons que l’ensemble des représentations fuchsiennes j telles qu’il existe une application (j,ρ)-équivariante et contractante de H2 dans M est un ouvert non vide et contractile de l’espace de Teichmüller (sauf lorsque ρ est elle-même fuchsienne). Ce résultat nous permet de décrire l’espace des métriques lorentziennes de courbure constante -1 sur un fibré en cercle au-dessus d’une surface compacte. Nous montrons que cet espace possède un nombre fini de composantes connexes classifiées par un invariant que nous appelons longueur de la fibre. Nous prouvons également que le volume total de ces métriques ne dépend que de la topologie du fibré et de la longueur de la fibre. / In this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of representations of surface groups into the isometry group of a complete simply connected Riemannian manifold M of curvature less than or equal to -1. Given such a representation ρ, we prove that the set of Fuchsian representations j for which there exists a (j,ρ)-equivariant contracting map from H2 to M is a non-empty open contractible subset of the Teichmüller space (unless ρ itself is Fuchsian). This result allows us to describe the space of Lorentz metrics of constant curvature -1 on a circle bundle over a closed surface. We show that this space has finitely many connected components, classified by an invariant that we call the length of the fiber. We also prove that the total volume of those metrics only depends on the topology of the bundle and on the length of the fiber.