In this work, we study geometrical and physical properties of exact spacetimes that belong to non-expanding Pleba'nski-Demia'nski class. It is a family of solutions of type D that also belong to the Kundt class, and contain seven arbitrary parameters including a cosmological constant. We present here the results of three extensive articles, each focusing on a different aspect of the problem. In the first article, we investigate the meaning of individual parame- ters in the non-expanding Pleba'nski-Demia'nski metric. First, we set almost all parameters to zero and obtain Minkowski and (anti-)de Sitter backgrounds. Af- terwards, we allow other parameters to be non-zero and we study the B-metrics, non-singular "anti-NUT" solutions and conclude with the full electrovacuum Pleba'nski-Demia'nski metric. In the second article, we focus on the de Sitter and anti-de Sitter backgrounds where we present and analyse 11 new diagonal metric forms of (anti-)de Sitter spacetime. We find five-dimensional parametriza- tions, draw coordinate surfaces and conformal diagrams. In the third article, we show that the AII-metric together with the BI-metric describes gravitational field around a tachyon on both Minkowski and (anti-)de Sitter backgrounds. Fi- nally, in order to better understand the global structure and...

In order to find quantum corrections to the de Sitter entropy, a new approach to higher loop Feynman integral computations on the sphere is presented. Arbitrary scalar Feynman integrals on a spherical background are brought into the generalized Euler integral (A-hypergeometric series/GKZ systems) form by expressing the massive scalar propagator as a bivariate radial Mellin transform of the massless scalar propagator in one higher dimensional Euclidean flat space. This formulation is expanded to include massive and massless vector fields by construction of similar embedding space propagators. Vector Feynman integrals are shown to be sums over generalized Euler integral formed of underlying scalar Feynman integrals. Granting existence of general spin embedding space propagators, general spin Feynman integrals are shown, by the construction of a "master" integral, to also be sums over generalized Euler integral representations of scalar Feynman integrals. Finding exact embedding space propagator expressions for fields of integer spin ≥ 2 and half integer spin is left to future work.

<p>This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries.</p><p>The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that the cross section of the cylinder has one cusp. We establish the meromorphic continuation of the extension of Eisenstein series and incomplete theta series through the limit set. Furthermore, we derive explicit formulas for the residues of the extension operator in terms of boundary values of automorphic eigenfunctions.</p><p>The motivation for the second paper comes from conformal geometry in Lorentzian signature. We prove the existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.</p>

<p>String theory is a unified framework for general relativity and quantum mechanics, thus being a theory of quantum gravity. In this thesis we discuss various aspects of quantum gravity for particular systems, having in common the existence of horizons. The main motivation is that one major challenge in theoretical physics today is in trying to understanding how time dependent backgrounds, with its resulting horizons and space-like singularities, should be described in a controlled way. One such system of particular importance is our own universe.</p><p>We begin by discussing the information puzzle in de Sitter space and consequences thereof. A typical time-scale is encountered, which we interpreted as setting the thermalization time for the system. Then the question of closed time-like curves is discussed in the combined setting where we have a rotating black hole in a Gödel-like universe. This gives a unified picture of what previously was considered as independent systems. The last three projects concerns $c=1$ matrix models and their applications. First in relation to the RR-charged two dimensional type 0A black hole. We calculate the ground state energy on both sides of the duality and find a perfect agreement. Finally, we relate the 0A model at self-dual radius to the topological string on the conifold. We find that an intriguing factorization of the theory previously observed for the topological string is also present in the 0A matrix model.</p>

String theory is a unified framework for general relativity and quantum mechanics, thus being a theory of quantum gravity. In this thesis we discuss various aspects of quantum gravity for particular systems, having in common the existence of horizons. The main motivation is that one major challenge in theoretical physics today is in trying to understanding how time dependent backgrounds, with its resulting horizons and space-like singularities, should be described in a controlled way. One such system of particular importance is our own universe. We begin by discussing the information puzzle in de Sitter space and consequences thereof. A typical time-scale is encountered, which we interpreted as setting the thermalization time for the system. Then the question of closed time-like curves is discussed in the combined setting where we have a rotating black hole in a Gödel-like universe. This gives a unified picture of what previously was considered as independent systems. The last three projects concerns $c=1$ matrix models and their applications. First in relation to the RR-charged two dimensional type 0A black hole. We calculate the ground state energy on both sides of the duality and find a perfect agreement. Finally, we relate the 0A model at self-dual radius to the topological string on the conifold. We find that an intriguing factorization of the theory previously observed for the topological string is also present in the 0A matrix model.

This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries. The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that the cross section of the cylinder has one cusp. We establish the meromorphic continuation of the extension of Eisenstein series and incomplete theta series through the limit set. Furthermore, we derive explicit formulas for the residues of the extension operator in terms of boundary values of automorphic eigenfunctions. The motivation for the second paper comes from conformal geometry in Lorentzian signature. We prove the existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.

Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry. / Graduate / 0986 / 0753 / jpbabb@yahoo.ca

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FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / A presente Tese compreende um exame crÃtico da estrutura de funcionamento do sistema do capital, à luz da contradiÃÃo central assinalada por Karl Marx nos Grundrisse. A contradiÃÃo vai se tornando visÃvel com a substituiÃÃo do trabalho vivo (trabalho humano direto) pelo trabalho morto (mÃquinas). Em decorrÃncia, esvazia-se a substÃncia do valor e os trabalhadores diretos sÃo reduzidos à condiÃÃo de apÃndice de mÃquinas que trabalham, restando-lhes as atividades de reguladores e de suportes para complexos automÃticos. O movimento lÃgico do valor e o transcurso histÃrico do processo de subsunÃÃo do trabalho ao capital, propiciam a hipÃtese de que o conjunto dos trabalhadores estaria sendo submetido a uma tendÃncia perversa que qualifica desqualificando suas aptidÃes e habilidades. Ao mesmo tempo, simplifica o trabalho e desvaloriza a forÃa-de-trabalho. A fim de averiguar tal processo de disrupÃÃo do mundo do trabalho, constituiu-se um objeto de pesquisa que permitisse checar a atuaÃÃo de trabalhadores tidos, pelo senso comum, como altamente qualificados. Eis a razÃo pela qual se tomou como plano investigativo, a âbusca dos egressos do CEFETCEâ no mercado de trabalho, centrando a investigaÃÃo nos haveres tecnolÃgicos de mecatrÃnicos e telemÃticos. A questÃo bÃsica à verificar atà que ponto esses operadores high-tech ativam a gama dos conhecimentos obtidos em sua formaÃÃo teÃrico-prÃtica cefeteana, no dia-a-dia das atividades profissionais. Foram entrevistados sessenta tecnÃlogos, alÃm de professores, administradores industriÃrios e operÃrios de fÃbrica vinculados a dÃspares ramos de produÃÃo de mercadorias. As entrevistas foram sempre secundadas por visitas a vÃrias plantas produtivas. Como resultado, o pesquisador foi premiado com um fÃrtil material sociolÃgico, prenhe de expressÃes simbÃlicas e de constructos tÃcnicos. A materialidade e a imaterialidade das experiÃncias, explÃcita e implicitamente vivenciadas, evidenciaram a âcontradiÃÃo em processoâ no coraÃÃo de sistemas de produÃÃo automÃticos. Nestes, estÃo reservados para os trabalhadores imediatos atos fetichistas como âcuidarâ (de mÃquinas), âassistirâ (linhas de produÃÃo), âolharâ (supervisÃrios) e âtrocar placasâ (eletrÃnicas) etc. / The present Thesis comprises a critical examination of the structure of the working of the system of the capital, in the light of the central contradiction indicated by Karl Marx in the Grundrisse. The expression of the contradiction gets visibility with the substitution for dead labor (machines) of live labor (human direct labor). Therefore, the substance of value becomes empty and the direct laborers are reduced to the condition of appendix of machines they work with, remaining to them the activities of regulating and supporting the automatic complexes. The logical movement of value and the historical course of the process of subsumption of labor to capital provide the hypothesis that the working class were being submitted to a perverse trend that qualifies in a disqualifying manner its aptitudes and abilities. At the same time, that process simplifies the labor and devaluates labor-force. In order to investigate such process of disruption of the world of labor it was crucial to choose an object of research that allowed checking the performance of workers recognized by common sense as highly qualified. That is the reason for which the âsearch of the egresses of the CEFETCEâ in the labor market was the core of the investigation. Technological assets of mechathronics and telematics technicians were investigate. The basic question of the inquiry is to verify to what extent these high-tech operators activate, the gamma of knowledge acquired during theoretical and practical formation at CEFETCE, to their everyday professional activities. Sixty technologists were interviewed, as well as, professors, industrial managers and laborers of various branches of merchandise production. The interviews always were seconded by visits to some productive plants. As a result, the researcher was awarded with a fertile sociological material, pregnant of symbolic expressions and technological constructs. The materiality and the immateriality of the experiences evidenced âthe contradiction in processâ in the heart of automatic systems of production. In those systems, fetishist production acts are set aside for the direct workers, in the form âcaring ofâ (machines), âwatchingâ (production lines), âlooking atâ (monitors) and âchanging platesâ (electronics) etc.

The subject of study of this thesis is the Kerr-Newman-(anti-)de Sitter space- time, a rotating and charged exact black-hole solution of the Einstein-Maxwell equations with a non-zero cosmological constant. In the first part of the thesis we examine admissible extremal configurations, present the corresponding Penrose diagrams, and investigate the effects of frame-dragging. In the second part, we follow the motion of charged particles via the Lagrangian formalism, focusing on the equatorial plane and the axis where we arrived at some analytic results con- cerning the trajectories. Static particles, effective potentials and - in the case of the equatorial plane - stationary circular orbits are examined. We also perform numerical simulations of particle motion to be able to check our analytic results and also to foster our intuition regarding the behaviour of the test particles. The last part concerns quantum tunnelling of particles through the space-time's hori- zons, specifically the null geodesic method. The main goal of these computations is to obtain horizon temperatures, in which we succeed up to a constant multi- plicative factor. We discuss various pitfalls of the method and stake out a possible approach when applying it to the extreme horizons present in KN(a)dS. 1