Depuis quelques années, le projet d’intégrer la physique einsteinienne dans le cursus scolaire soulève de l’intérêt grandissant dans la communauté des chercheurs en éducation en physique. D’après plusieurs chercheurs, pour mieux comprendre les sciences et les technologies d’aujourd’hui, les élèves ont besoin de connaissances de la physique moderne (Henriksen et al., 2014; Kaur, Blair, Moschilla, Stannard et Zadnik, 2017a). Pour Kaur et al. (2017), la visée éducative principale de l’enseignement des sciences est de faire apprendre aux élèves notre meilleure compréhension de l'univers afin de former les citoyens de demain (Kaur, Blair, Burman, et al., 2017). Puisque le concept de la gravité einsteinienne est absent du curriculum scolaire québécois, cette recherche vise à établir un portrait des recherches menées depuis les dernières années au sujet de l’enseignement et de l’apprentissage de la physique einsteinienne aux niveaux primaire et secondaire. Afin de répondre à cet objectif, la recherche utilise une approche provenant de la méthodologie de l’ingénierie didactique (Artigue, 1988a). Cette méthode a permis d’établir une liste des éléments à étudier. À partir de la recension des écrits et des arguments mobilisés par les tenants de l’enseignement de la physique einsteinienne, la recherche met en exergue les principaux enjeux de l’enseignement de la gravité einsteinienne et tente de comprendre et d’expliquer les avantages de son enseignement à l’école primaire et secondaire, exprimés par des chercheurs dans ce domaine. Les résultats de cette étude permettent d’avoir une image sur la situation actuelle de l’enseignement de la gravité einsteinienne. Ils sont regroupés et présentés selon trois thèmes: étude épistémologique du concept et de l’histoire de son développement; implications du concept de la gravité einsteinienne sur le développement des technologies et de la physique moderne, sur la compréhension de l’univers et sur le développement de la pensée scientifique; résultats de l’étude des recherches menées sur l’enseignement du concept de la gravité. Ce mémoire me permet de préparer une base théorique pour réaliser, dans mon projet doctoral, les trois autres étapes proposées par la méthodologie d’ingénierie didactique, soit l’élaboration, la réalisation et l’évaluation d’un dispositif d’enseignement du concept de gravité einsteinienne au 2e cycle du secondaire. Mots clés : physique einsteinienne, enseignement de la gravité einsteinienne, approches et méthodes d’enseignement de la physique, développement de la pensée scientifique

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: Entropy bounds arise from Black hole thermodynamics and are a significant departure from the conventional understanding of the information in a given region. This shift in paradigm is a consequence of the the fact that there is an unexpected relationship between the area and the entropy of a given region of spacetime. Entropy bounds are simplified formulations which are ultimately attempting to be developed into the complete and broad conjecture of the Holographic Principle. This hasn’t been achieved successfully as yet. In this thesis the aim is to introduce how the notion of an entropy bound was first suggested and it’s subsequent development into more robust formulations. The shortcomings of these conjectures are highlighted along with their strengths. A foundational introduction of the mathematical requirements for General Relativity is addressed along with an overview of Einstein’s theory of gravity. This is illustrated by showing the curvature of relative geodesics as being a consequence of gravity. This is contrasted with Newtonian theory where gravity is also shown to manifests as the curvature of relative geodesics. The working background is concluded with a discussion of Einstein’s field equations along with simple and common solutions often used and required. / AFRIKAANSE OPSOMMING: Swartgat Termodinamika impliseer grense op die entropie, en dus inligting, in ’n gegewe ruimtetyd volume, wat ’n drastiese afwyking van die tradisionele denkwyse oor inligting impliseer. Hierdie paradigma skuif het sy oorsprong in ’n onverwagte verband tussen die oppervlakte van, en entropie bevat, in ’n gegewe ruimte tyd volume. Entropie grense is eenvoudige formulerings van hierdie verwantskap wat uiteindelik beslag moet kry in die vollediger en wyer holografiese beginsel. Hierdie doelwit is nog nie bereik nie. Die doel van hierdie tesis is om die oorsprong en verdere formalisering van entropie grense te verduidelik. Beide die sterk en swak punte van die formulerings word bespreek. Algemene relatiwiteits teorie as ’n teorie van gravitasie, sowel as die wiskundige onderbou daarvan, word oorsigtelik bespreek. Die geometries onderbou van gravitasie word geillustreer aan die hand van die buiging van relatiewe geodete. Dit word met Newton se gravitasie teorie vergelyk wat ook in die buiging van relatiewe geodete gemanifesteer word. Hierdie oorsigtelike agtergrond word afgesluit met ’n oorsig van Einstein se vergelykings, asook eenvoudige en algemene oplossings wat dikwels nodig is en gebruik word.

General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in terms of their masses and spins in general relativity and which states that these compact objects are described by the Kerr metric. I investigate a quasi-Kerr metric and construct a Kerr-like spacetime, both of which contain an independent parameter in addition to mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric has to be zero. I show that already moderate changes of the deviation parameters in either metric lead to significant modifications of the observed signals. First, I apply this framework to the imaging of supermassive black holes using very-long baseline interferometry. I show that the shadow of a black hole as well as the shape of a bright and narrow ring surrounding the shadow depend uniquely on its mass, spin, inclination, and the deviation parameter. I argue that the no-hair theorem can be tested with observations of the supermassive black hole Sgr A*. Second, I investigate the potential of quasi-periodic variability observed in both galactic black holes and active galactic nuclei to test the no-hair theorem in two different scenarios. Third, I show that the profiles of relativistically broadened iron lines emitted from the accretion disks of black holes imprint the signatures of deviations from the Kerr metric. In the second part, I devise a method to test the predicted evaporation of black holes in the Randall-Sundrum model of string theory-inspired braneworld gravity through the orbital evolution of black-hole X-ray binaries and obtain constraints on the size of the extra dimension from A0620-00 and XTE J1118+480. I predict the first detection of orbital evolution in a black-hole binary.

We use recently published redshift space distortion measurements of the cosmological growth rate, f sigma(8)(z), to examine whether the linear evolution of perturbations in the R-h = ct cosmology is consistent with the observed development of large-scale structure. We find that these observations favour R-h = ct over the version of Lambda cold dark matter (Lambda CDM) optimized with the joint analysis of Planck and linear growth rate data, particularly in the redshift range 0 < z < 1, where a significant curvature in the functional form of f sigma(8)(z) predicted by the standard model-but not by R-h = ct-is absent in the data. When Lambda CDM is optimized using solely the growth rate measurements; however, the two models fit the observations equally well though, in this case, the low-redshift measurements find a lower value for the fluctuation amplitude than is expected in Planck Lambda CDM. Our results strongly affirm the need for more precise measurements of f sigma(8)(z) at all redshifts, but especially at z < 1.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2016. / The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS. / MT2016

Le paradigme ΛCDM est le modèle standard de la cosmologie. Dans ce modèle, l'univers est constitué aujourd'hui en majeure partie par de la matière noire froide (CDM) et la constante cosmologique Λ qui produit l'accélération cosmique. Cependant, ce modèle standard n'est pas entièrement complet. L'utilisation de la constante cosmologique introduit des problèmes théoriques dans une description de la théorie des champs quantiques et des indications observationnelles suggèrent que notre description à grande échelle de l'univers devrait être affinée. Ainsi, trouver des alternatives au modèle standard est d'une importance cruciale aujourd'hui. / The ΛCDM paradigm is the standard model of cosmology. In this model, the universe is constituted today for the major part by Cold Dark Matter along with the Cosmological Constant Λ that drives cosmic acceleration. However, this standard model is not fully complete. Using the Cosmological Constant introduces theoretical issues in a quantum field theory description and tentative observational evidences suggests our large scale description of the universe should be refined. Finding alternatives to the standard model is therefore of crucial importance today.

Nesta dissertação estudamos alguns aspectos da correspondência fluido/gravitação aplicada ao espaço plano em coordenadas de Rindler ingoing. Nosso principal objetivo é estudar o efeito de transformações de Ehlers e simetrias das equações de Einstein no contexto da correspondência fluido/gravitação. Para isso, fazemos uma revisão dos aspectos principais da Relatividade Geral e da Hidrodinâmica, os quais serão empregados ao longo do texto. Damos bastante atenção ao desenvolvimento de um método que permite encontrar soluções da equações de Einstein por meio de uma expansão em derivadas, o qual sera utilizado posteriormente para gerar uma solução-base sobre a qual aplicaremos transformações de Ehlers. Nós mostramos que a métrica de um espaçotempo plano em coordenadas de Rindler ingoing está relacionada a um espaçotempo de Taub por meio de uma transformação de Ehlers e nós utilizamos um método em que nós resolvemos a equação de Killing perturbativamente na expansão no parâmetro $\\epsilon$. Os resultados obtidos com este método não são inteiramente conclusivos, de modo que faz-se necessária uma futura investigação. / In this dissertation we study some aspects of the fluid/gravity correspondence applied to flat space in ingoing Rindler coordinates. Our main goal is to study the effect of Ehlers transformations and symmetries of the Einstein equations in the context of fluid/gravity correspondence. To do so, we review the main aspects of General Relativity and Hydrodynamics which will be employed throughout the text. We devote significant attention to a method that allows us to find solutions to the Einstein equations that by performing a derivative expansion, which will be utilized afterwards to generate our seed solution, upon which we later apply the Ehlers transformations. We show that the metric of flat spacetime in ingoing Rindler coordinates is related to a Taub spacetime by an Ehlers transformation and we utilize an approach in which we solve the Killing equation perturbatively in a parameter expansion. The results obtained by using this approach are not entirely conclusive, and further investigation is still required.

Estudamos a evolução temporal de perturbações escalares na vizinhança de uma estrela com densidade uniforme que colapsa em um buraco negro. O trabalho começa com um estudo básico de gravitação e modos quasi-normais. O objetivo principal é resolver a equação de Klein-Gordon sem massa para a perturbação escalar, cuja solução depende de métodos numéricos. Com este objetivo, tratamos os aspectos teóricos de buracos negros e estrelas a partir da solução prevista pela Relatividade Geral para um buraco negro, estrelas com densidade uniforme e estrelas em colapso. Estudamos também uma maneira de reduzirmos a Equação de Klein-Gordon para uma forma conveniente de ser integrada, assim como os métodos numéricos necessários para resolver essa equação. Encontramos soluções para os modos variando a massa M, o raio inicial R e o rótulo do momento angular l. Essas soluções são irregulares em muitas situações, mas em geral elas são crescentes, de acordo com o comportamente observado de explosões de Supernovas. / This work is a study on the time evolution of scalar perturbations around a star collapsing to a black hole. It starts with a basic study of gravitation and quasi-normal modes. The aim is to derive the solution of the massless Klein-Gordon equation, that depends on numerical methods. Aiming at this goal, we studied theoretical aspects of stars, black holes and gravitational collapse. The methods include coordinate substitutions to modify the Klein-Gordon equation to a simple form. We also studied numerical methods for partial differential equations. Solutions of the quasi-normal modes were found with different values of M, R and l. The solutions are irregular in several situations, but some of them display increasing modes, that could be explained by the explosive behavior of Supernovas.

Cerca de 25% do conteúdo energético do universo se encontra sob uma forma de natureza ainda não determinada e é conhecida pelo nome de matéria escura. Desde as primeiras especulações acerca de sua existência (Zwicky ~ 1933), vários modelos foram propostos na tentativa de justificar os dados observacionais encontrados mas, até hoje, nenhum deles foi capaz de cumprir essa tarefa a contento. Nesta dissertação, apresentaremos uma breve discussão desses modelos, além de propor um novo, baseado na idéia de que tanto a matéria escura quanto a energia escura possam ser compostas pelo campo escalar de Born-Infeld. / Nearly twenty five percent of the energetic content of the universe appears in a form that is still unknown and is named dark matter. Since the first speculations about its existence (Zwicky ~1933), many models have been proposed trying to justify all the observed data but, until now, none of them has been able to solve this problem. In this monography, we will present a brief discussion about these models and propose a new one, based on the idea that both dark matter and dark energy could be the Born Infeld scalar field.

O papel da torção do espaço-tempo na Relatividade Geral é revisto nesta tese. Estudando-se formas diferenciais de volume em variedades afins, será mostrado que o elemento de volume riemanniano usual não é compatível com conexões com torção. Um novo elemento de volume é proposto e usado na formulação lagrangiana da gravitação de Einstein-Cartan. O modelo que surge prevê, entre outras coisas, a propagação da torção e a interação entre campos de gauge e a torção do espaço-tempo sem a perda da simetria de gauge. O novo elemento de volume também permite uma interpretação geométrica, em termos das quantidades não-riemannianas do espaço-tempo, para as correções à gravitação advindas da teoria de cordas (dilaton gravity). / The role of space-time torsion in General Relativity is reviewed in this thesis. Through the analysis of volume forms in affine manifolds, it will be shown that the usual riemannian volume element is no! compatible with connections with non-vanishing torsion. A new volume element is proposed and used in the lagrangian formulation for Einstein-Cartan theory of gravity. By this new model, torsion can propagate and gauge fields can interact with torsion without breaking of gauge invariance. The new volume element can also provide a geometrical interpretation for the dilaton gravity by means of the non-riemannian quantities of space-time.