Le mécanisme d'instabilité gravitationnelle d'un champ de Yang-Mills est étudié via l'intégration numérique de la formulation hamiltonienne du système Einstein-Yang-Mills décrivant le couplage d'un champ de jauge à la gravitation. Une évolution en deux temps est mise en évidence: une dilution des fluctuations, conséquence de l'invariance conforme du champ, apparaît en premier lieu ; elle est suivie d'un régime d'oscillations croissantes lorsque l'on s'éloigne suffisamment de la solution homogène. Une comparaison instructive avec le mécanisme d'instabilité gravitationnelle du champ scalaire est également envisagée. Enfin, nous avons étudié l'influence de champs scalaires de quintessence sur la formation d'amas de matière noire grâce à la modification d'un code à N particules. Ceux-ci inhibent la formation des amas, en privilégiant des structures moins nombreuses et de faible masse, tout en produisant des différences assez significatives que pour permettre de discerner non seulement un modèle avec quintessence d'un autre plus conventionnel (avec constante cosmologique) mais également les divers modèles de quintessence entre eux. / The gravitational instability of Yang-Mills fields is studied by means of a numerical integration of the hamiltonian formulation of Einstein-Yang-Mills equations, which describe the coupling between gravitation and a gauge field. A two-step evolution appears to rule this mechanism: the fluctuations first dilute, as a sequel of the conformal invariance of the gauge theory; then, the fluctuations undergo oscillations of increasing amplitude as the solution moves away from the homogeneous one. An interesting comparison with the gravitational instability of a scalar field has also been made. Finally, we have established that the quintessence scalar fields inhibit the formation of dark matter halos. By analysing the results of a modified N-body code, we show that those fields produce less structures and lighter halos, and lead to significative differences that allow to distinguish either a quintessence scenario from a more conventional one with a cosmological constant either different quintessence models.

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.

Einstein's field equations are extremely difficult to solve, and when solved, the solutions are even harder to understand. In this thesis, two analysis tools are developed to explore and visualize the curvature of spacetimes. The first tool is based on a thorough examination of observer independent curvature invariants constructed from different contractions of the Riemann curvature tensor. These invariants are analyzed through their gradient fields, and attention is given to the resulting flow and critical points. Furthermore, we propose a Newtonian analog to some general relativistic invariants based on the underlying physical meaning of these invariants, where they represent the cumulative tidal and frame-dragging effects of the spacetime. This provides us with a novel and intuitive tool to compare Newtonian gravitational fields to exact solutions of Einstein's field equations on equal footing. We analyze the obscure Curzon-Chazy solution using the new approach, and reveal rich structure that resembles the Newtonian gravitational field of a non-rotating ring, as it has been suspected for decades. Next, we examine the important Kerr solution, which describes the gravitational field of rotating black holes. We discover that the observable part of the geometry outside the black hole's event horizon depends significantly on its angular momentum. The fields representing the cumulative tidal and frame-dragging forces change qualitatively at seven specific values of the dimensionless spin parameter of the black hole. The second tool we develop in this thesis is the accurate construction of the Penrose conformal diagrams. These diagrams are a valuable tool to explore the causal structure of spacetimes, where the entire spacetime is compactified to a finite size, and the coordinate choice is fixed such that light rays are straight lines on the diagram. However, for most spacetimes these diagrams can only be constructed as a qualitative guess, since their null geodesics cannot be solved. We developed an algorithm to construct very accurate Penrose diagrams based on numeric solutions to the null geodesics, and applied it to the McVittie metric. These diagrams confirmed the long held suspicion that this spacetime does indeed describe a black hole embedded in an isotropic universe. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-30 14:02:55.865

We first consider four-dimensional gauge theory on twistor space, taking as a case study maximally supersymmetric Yang-Mills theory. Using a twistor action functional, we show that gauge theory scattering amplitudes are naturally computed on twistor space in a manner that is much more efficient than traditional space-time Lagrangian techniques at tree-level and beyond. In particular, by rigorously studying the Feynman rules of a gauge-fixed version of the twistor action, we arrive at the MHV formalism. This provides evidence for the naturality of computing scattering amplitudes in twistor space as well as an alternative proof of the MHV formalism itself. Next, we study other gauge theory observables in twistor space including gauge invariant local operators and Wilson loops, and discuss how to compute their expectation values with the twistor action. This enables us to provide proofs for the supersymmetric correlation function / Wilson loop correspondence as well as conjectures on mixed Wilson loop - local operator correlators at the level of the loop integrand. Furthermore, the twistorial formulation of such observables is naturally algebro-geometric; this leads to novel recursion relations for computing mixed correlators by performing BCFW-like deformations of the observables in twistor space. Finally, we apply these twistor actions to gravity. Using the on-shell equivalence between Einstein and conformal gravity in de Sitter space, we argue that the twistor action for conformal gravity should encode the tree-level graviton scattering amplitudes of Einstein's theory. We prove this in terms of generating functionals, and derive the flat space MHV amplitude as well as a recursive version of the MHV amplitude with cosmological constant. We also include some discussion of super-connections and Coulomb branch regularization on twistor space.

Einstein's equations in vacuum spacetimes with two spacelike killing vectors are explored using affine projection tensor geometry. By doing a semi-conformal transformation on the metric, a new "fiducial" geometry is constructed using a projection tensor fields. This fiducial geometry provides coordinate independent information about the underlying structure of the spacetime without the use of an explicit form of the metric tensor.

Einstein’s equations are derived by following Jacobson’s thermodynamic method. It is seen that a family of possible field equations exist which satisfy the thermodynamic argument. Modified theories of gravity are addressed as possible candidates for replacing dark matter as an explanation for anomalous cosmological phenomena. Many of the proposed modified theories are not powerful enough to explain the currently observed phenomena and are rejected as viable theories of gravity. A surviving candidate, TeVeS, is further analyzed under the aforementioned thermodynamic argument to check for its consistency with thermodynamics.

Spinning-particle motion is studied, within the pole-dipole approximation, in algebraically special space-times of type N, III and D. The spin-curvature interaction is analysed for the Pirani and Tulczyjew spin supplementary conditions; for N and D types, the condition is related to a relative acceleration of two near observers separated in the direction of particle's spin. For Tulczyjew's condition, the momentum-velocity relation is also studied as well as its consequences for the spin-curvature interaction. Finally, the type of motion is mentioned for which both the supplementary conditions considered are equivalent.

On étudie dans cette thèse le système d'Einstein-Lichnerowicz, aussi appelé système des contraintes conformes. C'est un système d'équations aux dérivées partielles nonlinéaires elliptiques, obtenu après application de la méthode conforme, qui intervient en théorie de la Relativité Générale, plus précisément dans l'analyse des équations d'Einstein comme un problème d'évolution.Le résultat principal de notre thèse, démontré en toutes dimensions supérieures ou égales à 3, est un résultat de stabilité du système des contraintes conformes. Il exprime la dépendance continue de l'ensemble des solutions du système des contraintes conformes en les grandeurs physiques de la méthode conforme. En ce sens, c'est un résultat de structure sur l'ensemble des solutions du système d'Einstein-Lichnerowicz.Ce résultat exprime aussi la pertinence physique d'une construction physique naturelle qui intervient dans le cadre de la méthode conforme, que nous appelons dans le manuscrit construction de Choquet-Bruhat-Geroch-Lichnerowicz et que nous décrivons en détail.Nous obtenons aussi dans cette thèse des résultats d'existence pour le système d'Einstein-Lichnerowicz. Un premier résultat d'existence est obtenu par des méthodes non-variationnelles. Un résultat indépendant de multiplicité est obternu comme conséquence du résultat de stabilité énoncé plus haut. / We investigate in this work the Einstein-Lichnerowicz constraints system, also called conformal constraints system. It is an elliptic system of nonlinear partial differential equations obtained through the conformal method, and arising in Mathematical General Relativity in the analysis of the Einstein equations as an evolution problem.Our main result, proven in any dimension greater than 3, is a stability result for the conformal constraints system. It asserts the continuous dependence of the set of solutions of the conformal constraints system in the physical parameters of the conformal method. It is then a structure result on the set of solutions of the Einstein-Lichnerowicz constraints system.Our result can be rephrased in terms of the physical relevance of a physical construction naturally arising in the context of the conformal method, that we call Choquet-Bruhat-Geroch-Lichnerowicz formalism and that we describe in detail.We also obtain in this work existence results for the Einstein-Lichnerowicz constraints system. A first existence result is obtained via non-variational methods. An independent multiplicity result is obtained as a consequence of the aforementioned stability result.

The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was shown that the corresponding constraint violations subside after a few orbits, becoming comparable to those found in evolutions of standard conformally flat, helically symmetric binary initial data. This dissertation presents the first spinning neutron star binary simulations in circular orbits with a orbital eccentricity less then 0.01. The initial data sets corresponding to binaries with spins aligned, zero and anti-aligned with the orbital angular momentum were evolved in time. These simulations show the orbital “hang-up” effect previously seen in binary black holes. Additionally, they show orbital eccentricities that can be up to one order of magnitude smaller than those found in helically symmetric initial sets evolutions. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2013.

Desenvolvemos aqui um estudo das formulações alternativas-equivalentes da Relatividade Geral, baseada no formalismo de conexões de Ashtekar. Iniciamos discutindo a estrutura matemática necessária de fibrados e conexões, e a teoria de sistemas Hamiltonianos vinculados. Em seguida, damos uma breve introdução ao formalismo métrico de Einstein e então passamos ao formalismo geometrodinâmico canônico (formalismo ADM). Introduzimos as transformações no espaço de fase que geram as formulações alternativas, de forma generalizada tal que possamos obter ambas as variáveis complexas de Ashtekar ou as variáveis reais de Barbero, ou mesmo qualquer forma intermediária por meio do parâmetro de Immirzzi. / We develop here a study of the alternative-equivalent formulations of General Relativity, based on Ashtekars connexion formalism. We begin discussing the mathematical structure needed of fibre bundles and connexions, and the theory of constrained Hamiltonian systems. Next, we give a brief introduction for Einsteins metric formalism and then we pass to the canonical geometrodynamic formalism (ADM formalism). We introduce the transformations of the phase space which generate the alternative formulations, in a generalized form such that we can obtain both Ashtekars complex variables or Barberos real variables, or even any intermediary form by using the Immirzzi parameter.