Dans cette thèse, nous étudions la structure asymptotique de la gravité à trois dimensions d’espace-temps avec et sans constante cosmologique.La première partie de la thèse présente en détails les propriétés fondamentales de la gravité à trois dimensions pour des espaces à constante cosmologique négative, ou espaces de types Anti-de Sitter (AdS). Nous introduisons le formalisme de Chern-Simons pour la gravité en utilisant la formulation dite du premier ordre pour cette dernière. Nous présentons également les conditions aux bords dites de Brown-Henneaux et le calcul associé de l’algèbre des charges de surface. Enfin, nous décrivons les étapes de la réduction du modèle de Chern-Simons à un modèle de Wess-Zumino-Witten puis à celui d’une théorie de Liouville. La relevance de cette théorie dans le calcul microscopique de l’entropie d’un trou noir à trois dimensions est également discutée.La seconde partie de la thèse contient les contributions originales. Tout d’abord, nous étendons l’analyse de la dynamique asymptotique de la supergravité à trois dimensions au cas d’une constante cosmologique nulle. Nous montrons que l’algèbre des charges de surface associée est une extension supersymétrique de l’algèbre BMS, et construisons la théorie bidimensionnelle située au bord de l’espace-temps qui possède cette symétrie. Le second résultat est l’obtention d’une symétrie de dimension infinie au voisinage de l’horizon d’événements d’un trou noir tridimensionnel non extrême. Troisièmement, nous discutions le cas d’une constante cosmologique positive et montrons l’existence d’une théorie de Liouville euclidienne duale à la gravité d’Einstein avec des conditions aux bords de Dirichlet dans le patch statique. Enfin, nous explorons un autre cadre dans lequel des symétries de dimension infinie apparaissent pour des espaces temps qui non sont pas du type Anti-de Sitter. Nous considérons pour cela des déformations de ces derniers, connus sous le nom d’espaces-temps Warped Anti-de Sitter. Nous montrons que ces déformations admettent une algèbre de surface donnée par une somme semi-direct entre une algèbre de Virasoro et une algèbre affine de Kac-Moody, avec extensions centrales non nulles. Nous montrons que les configurations du trou noir hôte des espaces-temps Warped s’organisent en termes de deux algèbres de Virasoro. Nous identifions les générateurs associés qui décrivent les représentations de la théorie duale et, en appliquant une formule de Cardy, nous prouvons qu’un calcul microscopique reproduit correctement l’entropie de ces trous noirs. Nous étendons ce résultat à des conditions aux bords plus générales qui incluent de nouvelles solutions associés à des degrés de liberté locaux, des gravitons massifs contenus dans le volume d’espace-temps. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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This dissertation covers two di erent but related topics: the construction of new black hole solutions and the study of the microscopic origin of black hole entropy. In the solution part, two di erent sets of new solutions are found. The rst concerns a Plebanski-Demianski type solution in the ve-dimensional pure Einstein gravity, and the second concerns a three-charge (two of which equal) two-rotation solution to the ve-dimensional maximal supergravity. Obtaining new and interesting black hole solutions is an important and challenging task in studying general relativity and its extensions. During the past decade, the solutions become even more important because they might nd applications in the study of the gauge/gravity duality, which is currently in the central stage of the quantum gravity research. The Kerr/CFT correspondence is a recently propose example of the gauge/gravity duality. In the entropy part, we explicitly show that the Kerr/CFT correspondence can be applied to all known extremal stationary and axisymmetric black holes. We improve over previous works in showing that this can be done in a general fashion, rather than testing di erent solutions case by case. This e ort makes it obvious that the common structure of the near horizon metric for all known extremal stationary and axisymmetric black holes is playing a key role in the success of the Kerr/CFT correspondence. The discussion is made possible by the identi cation of two general ans atze that cover all such known solutions.

In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in d dimensions with and without a cosmological constant.<p><p>The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions.<p><p>The second part of this thesis contains the original contributions.<p>Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure particularly transparent, and constitute the main original result of the thesis.<p>Secondly, asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner in $d$ dimensions. In agreement with a recent conjecture, a Virasoro-Kac-Moody type algebra is found not only in three dimensions but also in the four dimensional asymptotically flat case.<p><p>These two parts of the thesis are supplemented by appendices. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Un des grand défis de la physique actuelle est la quantification de la gravit é. La théorie d’Einstein est remarquable pour ses prédictions. Malheureusement, elle reste une théorie classique et de ce fait en désaccord avec les progrès actuels en physique des particules qui montrent qu’à faible distance, une théorie physique doit être quantique. Une des pistes pour résoudre ce problème est d’étudier la version classique de la gravité dans l’espoir d’en déduire des propriétés ou même la forme de la théorie quantique.<p><p>Un des outils pour étudier une theorie est la notion de dualité. On dit que deux théories sont duales quand elles décrivent le même système par des moyens différents. La dualité est le dictionnaire permettant de passer d’une description à l’autre. Dans ma thèse, j’ai étudié deux dualités s’appliquant à la gravité en 4 dimensions.<p><p>La première est connue sous le nom de dualité électromagnétique. A l’origine, cette dualité s’applique à l’électromagnétisme où elle échange les rôles du champ & / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The present thesis is divided into three parts. In Part I we address a problem within Higher-Spin Gauge Theory in dimension three: namely, that of computing the asymptotic symmetry algebra of supersymmetric models, describing an infinite spectrum of integer and half-integer higher-spin fields. In Part II we investigate higher-spin theories in dimension four or greater, where we classify the consistent cross interactions between free gauge fermions of arbitrary spin and a photon or a graviton. A third part supplements the bulk of the manuscript with technical appendices. <p><p>Part I is concerned with the Higher-Spin Theory extending the anti-de Sitter orthosymplectic Supergravity in three dimensions. After recalling the construction of the latter we exhibit the structure of the former, and then explain how to generalize the boundary conditions for Supergravity to the higher-spin case. Following the usual procedure, we compute the form of the residual gauge parameter and then identify the Poisson-bracket algebra governing the asymptotic dynamics. It is found to be a nonlinear, supersymmetric algebra of the W-infinity type with same central charge as pure Gravity in the Virasoro sector, which is a subalgebra thereof. The simply supersymmetric case is treated explicitly whereas the details of the extended cases are relegated to the appendices. <p><p>Part II deals with the interaction problem for gauge fermions coupled to Electromagnetism and Gravity in flat spacetime of arbitrary dimension. First we recall the so-called BRST-Antifield techniques, which reformulate the deformation problem as a cohomological one, recasting the familiar Noether procedure for finding out interactions in a mathematically systematic way. We then use these methods to classify and obtain expressions for the gauge-invariant cubic couplings between a symmetric tensor-spinor and a spin-1 and spin-2 gauge field. With no input from previous works, we find the complete list of interaction terms with minimal assumptions and in particular shed light on the quartic obstructions to full consistency. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices.<p><p>The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism.<p>The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described.<p><p><p>The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry group of radiating asymptotically flat spacetimes. It has recently received renewed interest in the context of the flat holography and the infrared structure of gravity. In this thesis, we investigate the consequences of considering extensions of the BMS group in four dimensions with superrotations. In particular, we apply the covariant phase space methods on a class of first order gauge theories that includes the Cartan formulation of general relativity and specify this analysis to gravity in asymptotically flat spacetime. Furthermore, we renormalize the symplectic structure at null infinity to obtain the generalized BMS charge algebra associated with smooth superrotations. We then study the vacuum structure of the gravitational field, which allows us to relate the so-called superboost transformations to the velocity kick/refraction memory effect. Afterward, we propose a new set of boundary conditions in asymptotically locally (A)dS spacetime that leads to a version of the BMS group in the presence of a non-vanishing cosmological constant, called the Λ-BMS asymptotic symmetry group. Using the holographic renormalization procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we construct the phase space of Λ-BMS and show that it reduces to the one of the generalized BMS group in the flat limit. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished