Estudamos a entropia em várias situações na gravidade, verificando se seu comportamento é holográfico, obedecendo à lei de área de Bekenstein. Inicialmente, usando o método da \"parede de tijolos\", calculamos, em diversos casos, a entropia estatística de um campo escalar num fundo não trivial. Tal fundo é gerado por buracos negros de 4 ou 5 dimensões com cargas. A fórmula da entropia de Bekenstein é geralmente satisfeita, mas algumas correções são discutidas no caso pentadimensional. Este método é também aplicado para soluções tipo buracos negros na gravidade de Lovelock. Resulta que o método de \"parede de tijolos\", apesar de correto para a teoria de Einstein-Hilbert, pode não ser válido em geral, o que também acontece com a lei área. Algumas propriedades concernentes à teoria de cordas, especialmente a tecnologia das D-branas, são revistas naqueles aspectos necessários para este trabalho. Também estudamos e calculamos o limite superior da entropia para a gravidade de Lovelock. Finalmente, verificamos a validade do princípio holográfico num universo de (4 + n) dimensões numa fase inflacionária assimétrica. / We study the entropy for various situations in gravity, checking whether its behavior is holographic, obeying Bekensteins area law. First, using the brick wall method, we compute the statistical entropy of a scalar field in a nontrivial background in different cases. Such a background is generated by four and five dimensional black holes with charges. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case. This method is applied also to the black hole solutions of the Lovelock gravity. It turns out that the brickwall method, through correct for the Einstein-Hilbert theory, may fail in general. The same happens to the area law. Some properties concerning string theory, especially the D-branes technology, are reviewed while necessary to this work. Furthermore, we study and compute the upper limit of the entropy for the Lovelock gravity. Finally, we check the validity of the holographic principle in a (4+n) dimensional universe in an asymmetric inflationary phase.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 134-138).

Estudamos a entropia em várias situações na gravidade, verificando se seu comportamento é holográfico, obedecendo à lei de área de Bekenstein. Inicialmente, usando o método da \"parede de tijolos\", calculamos, em diversos casos, a entropia estatística de um campo escalar num fundo não trivial. Tal fundo é gerado por buracos negros de 4 ou 5 dimensões com cargas. A fórmula da entropia de Bekenstein é geralmente satisfeita, mas algumas correções são discutidas no caso pentadimensional. Este método é também aplicado para soluções tipo buracos negros na gravidade de Lovelock. Resulta que o método de \"parede de tijolos\", apesar de correto para a teoria de Einstein-Hilbert, pode não ser válido em geral, o que também acontece com a lei área. Algumas propriedades concernentes à teoria de cordas, especialmente a tecnologia das D-branas, são revistas naqueles aspectos necessários para este trabalho. Também estudamos e calculamos o limite superior da entropia para a gravidade de Lovelock. Finalmente, verificamos a validade do princípio holográfico num universo de (4 + n) dimensões numa fase inflacionária assimétrica. / We study the entropy for various situations in gravity, checking whether its behavior is holographic, obeying Bekensteins area law. First, using the brick wall method, we compute the statistical entropy of a scalar field in a nontrivial background in different cases. Such a background is generated by four and five dimensional black holes with charges. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case. This method is applied also to the black hole solutions of the Lovelock gravity. It turns out that the brickwall method, through correct for the Einstein-Hilbert theory, may fail in general. The same happens to the area law. Some properties concerning string theory, especially the D-branes technology, are reviewed while necessary to this work. Furthermore, we study and compute the upper limit of the entropy for the Lovelock gravity. Finally, we check the validity of the holographic principle in a (4+n) dimensional universe in an asymmetric inflationary phase.

Dans les dernières décennies, un modèlecosmologique, dénommé “modèle ACDM” ,a émergé et plusieurs observations ont montréqu’il est consistant avec les données. Toutefois, ilsexistent des problèmes encore ouverts ; en particuliernous ne connaissons pas la cause de l’accélérationobservée de l’expansion de l’Univers. De nombreuxmodèles alternatifs ont été proposés.Cette thèse traite d’une approche pour contraindreles alternatives au modèle ACDM dénommée “EffectiveTheory of Dark Energy”. Elle s’applique àtoutes les théories où un seul degré de liberté scalaireest ajouté aux deux degrés de liberté de la RelativitéGénérale. Ces théories sont appelées “théoriestenseur-scalaire”.Le chapitre 1 résume la plus générale classe de théoriestenseur-scalaire viables actuellement connue.Le chapitre 2 introduit la théorie efficace de l’énergienoire. L’inclusion dans la théorie efficace descouplages généraux entre le secteur gravitationnelle(métrique et champ scalaire) et la matière est décritdans le chapitre 3. Ceci inclut aussi la possibilitéque différentes espèces interagissent de façondifférente avec la gravité. La possibilité d’analyseren détail la stabilité de la théorie est explicité dansle chapitre 4.Un objectif de cette thèse est aussi l’investigationdes effets observables des déviations du modèleLCDM. Le chapitre 5 considère la possibilité d’uneinteraction entre la matière noire et l’énergie noire.Ce chapitre étudie les effets d’une telle interactionet, plus généralement, analyse la capacité des observationsfutures à imposer des contraintes sur lesparamètres libres de la théorie efficace. Le chapitre 6 se concentre sur les effets observationnels de lathéorie “ beyond-Horndeski” , en démontrant quedans ce théorie il existe un melange cinétique entrela matière et le champ scalaire. Ce melange donnelieu à un effets particuliers: l’affaiblissement de lagravité aux échelles des grands structures. / In the last decades, a cosmological model that fits observations through a vast range of scales emerged. It goes under the name of ACDM. However, there are still challenging questions that remain unanswered by this model, such as what causes the observed accelerated expansion of the universe. Hence, many alternative models have been proposed. This thesis concerns an approach to test such models known as “Effective Theory of Dark Energy” . It applies to all models where general relativity is modified by adding a single scalar degree of freedom, called “ scalar-tensor theories”. In Chapter 1 I introduce the most general classof such theories currently known. In Chapter 2, I resume the Effective theory of dark energy. The inclusion of a general coupling between matter and the gravitational sector is the subject of Chapter 3. Chapter 4 analyses in details the stability of different classes of theories.Another goal of the thesis is to study the observable effects of deviations from ACDM. In Chapter5, I consider the possibility of an interaction between dark matter and dark energy and I analyse the constraining power of future surveys on the free parameters of the theory. Chapter 6 focuses on the observational effects of theories where a kinetic mixing between matter and the scalar field exists.This gives a peculiar effect, namely the weakening of gravity at large scale structure scales.

This thesis is concerned with the description of macroscopic geometries through Loop Quantum Gravity, and there particularly with the description of cosmology within full Loop Quantum Gravity. For this purpose we depart from two distinct (classically virtually equivalent) ansätze: One is phase space reduction and the other is the restriction to particular states. It turns out that the quantum analogue of these two approaches are fundamentally different: The quantum analogue of phase space reduction needs the reformulation in terms of the observable Poisson algebra, so it can be applied to the noncommutative quantum phase space: It rests on the observation that the observable Poisson algebra of classical canonical cosmology is induced by the embedding of the reduced cosmological phase space into the phase space of full General Relativity. Using techniques related to Rieffel-induction, we develop a construction for a noncommutative embedding that has a classical limit that is described by a Poisson embedding. To be able to use this class of noncommutative embeddings for Loop Quantum Gravity, one needs a complete group of diffeomorphisms for the quantum theory, which is constructed. These two results are applied to construct a quantum embedding of a cosmological sector into full Loop Quantum Gravity. The embedded cosmological sector turns out to be discrete, like standard Loop Quantum Cosmology and can be interpreted as a super-selection sector thereof; however due to pathologies of the dynamics of full Loop Quantum Gravity, one can not induce a meaningful dynamics for this cosmological sector. The quantum analogue of restricting the space of states is achieved by explicitly constructing states for Loop Quantum Gravity with smooth geometry. These states do not exist within the Hilbert space of Loop Quantum Gravity, but as states on the observable algebra of Loop Quantum Gravity. This observable algebra is built from spin network functions, area operators and a restricted set of fluxes. For this algebra to be physically complete, we needed to construct a version of Loop Quantum Geometry based on a fundamental area operator. This version of Loop Quantum Geometry is constructed. Since the smooth geometry states are not in the Hilbert space of standard Loop Quantum Gravity, we needed to calculate the Hilbert space representation that contains them using the GNS construction. This representation of the observable algebra can be illustrated as a classical condensate of geometry with quantum fluctuations thereon. Using these representations we construct a quantum-minisuperspace, which allows for an interpretation of standard Loop Quantum Cosmology in terms of these states and led us to conjecture a new approach for the implementation of dynamics for Loop Quantum Gravity. / Die vorliegende Arbeit ist mit der Beschreibung makroskopischer Geometrien durch Schleifengravitation befasst und zwar insbesondere mit der Beschreibung von Kosmologie innerhalb der vollen Schleifengravitation. Für dieses Ziel verwenden wir zwei unterscheidliche (jedoch auf klassischem Level scheinbar äquivalente) Ansätze: Einerseits betrachten wir die Reduktion des Phasenraumes und andererseits die Beschränkung auf bestimmte Zustände. Es stellt sich jedoch heraus, dass sich die Quantenanaloga dieser beiden Zugänge fundamental unterscheiden: Das Quantenanalogon der Phasenraumreduktion muss als Aussage über die Observablen-Poissonalgebra umformuliert werden bevor sie auf den nichtkommutativen Phasenraum von Quantentheorien angewendet werden kann: Die zugrundeliegende Beobachtung ist, dass die Observablen-Poissonalgebra von klassischer kanonischer Kosmologie durch die Einbettung des kosmologischen Phasenraumes in den Phasenraum der Allgemeinen Relativitätstheorie induziert wird. Damit können wir eine Technik, die von der Rieffelinduktion abgeschaut ist, anwenden um die Konstruktion einer nichtkommutativen Einbettung zu entwickeln, welche sich im klassischen Limes zu einer Poissoneinbettung reduziert. Um diese Konstruktion der Einbettung auf die Schleifenquantengravitation anwenden zu können benötigt man eine vollständige Diffeomorphismengruppe für die Quantentheorie, welche erarbeitet wird. Diese beiden Ergebnisse werden angewendet um die Quanteneinbettung eines kosmologischen Sektors in die volle Schleifengravitation zu konstruieren. Dieser ist, wie die standard Schleifenkosmologie diskret und kann als Auswahlsektor derselben interpretiert werden; aufgrund von Pathologien in der Dynamik der vollen Schleifengravitation lässt sich aus dieser jedoch keine sinnvolle Dynamik für den kosmologischen Sektor induzieren. Das Quantenanalogon der Beschränkung des Raumes der Zustände basiert auf der expliziten Konstruktion von Zuständen, die eine glatte räumliche Geometrie beschreiben. Diese Zustände existieren zwar nicht im Hilbertraum der Schleifenquantengravitation, aber als Zustände auf der Observablenalgebra der Schleifenquantengravitation. Diese Observablenalgebra wird aus den Spinnetzwerken, den Flächenoperatoren und einer eingeschränkten Menge der Flüsse konstruiert. Um zu zeigen, dass diese Observablenalgebra physikalisch vollständig ist benötigen wir eine Schleifenquantengeometrie, die auf einem fundamentalen Flächenoperator aufbaut. Diese Schleifenquantengeometrie wird konstruiert. Nachdem die Zustände mit glatter Geometrie nicht im Hilbertraum der standard Schliefengravitation liegen, müssen wir aus diesen Zuständen Hilbertraumdarstellungen der Observablenalgebra durch die GNS-Konstruktion erschaffen. Diese Darstellung kann mit dem Bild eines klassichen Kondensats von Geometrie, um welches Quantenfluktuationen existieren, illustriert werden. Ausgehend von diesen Darstellungen konstruieren wir einen Quanten-Minisuperraum, welcher eine Interpretation der standard Schleifenkosmologie durch diese Zustände erlaubt. Dieser Zugang gab uns ausserdem den Hinweis auf eine mögliche Konstruktion einer Dynamik für die volle Schleifenquantengravitation.

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, 2014. / No abstract supplied.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. April 2013 / We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N = 4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.

Extr. de: Diss.--Physique--Aachen--Technischen Hochschule, 2001. / Notes Bibliogr.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 131-133).

Thesis (M.Sc.) -- University of Adelaide, Dept. of Mathematical Physics, 1977.