Teorias f(R) de gravidade na formulação de Palatini

In this dissertation, after a brief review on the Einstein s General Relativity Theory and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models, we present and discuss the alternative theories of gravity dubbed f(R) gravity. These theories come about when one substitute in the Einstein-Hilbert action the Ricci curvature R by some well behaved nonlinear function f(R). They provide an alternative way to explain the current cosmic acceleration with no need of invoking neither a dark energy component, nor the existence of extra spatial dimensions. In dealing with f(R) gravity, two different variational approaches may be followed, namely the metric and the Palatini formalisms, which lead to very different equations of motion. We briefly describe the metric formalism and then concentrate on the Palatini variational approach to the gravity action. We make a systematic and detailed derivation of the field equations for Palatini f(R) gravity, which generalize the Einsteins equations of General Relativity, and obtain also the generalized Friedmann equations, which can be used for cosmological tests. As an example, using recent compilations of type Ia Supernovae observations, we show how the f(R) = R − fi/Rn class of gravity theories explain the recent observed acceleration of the universe by placing reasonable constraints on the free parameters fi and n. We also examine the question as to whether Palatini f(R) gravity theories permit space-times in which causality, a fundamental issue in any physical theory [22], is violated. As is well known, in General Relativity there are solutions to the viii field equations that have causal anomalies in the form of closed time-like curves, the renowned Gödel model being the best known example of such a solution. Here we show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with density and pressure p that satisfy the weak energy condition + p 0 is necessarily isometric to the Gödel geometry, demonstrating, therefore, that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We derive an expression for a critical radius rc (beyond which causality is violated) for an arbitrary Palatini f(R) theory. The expression makes apparent that the violation of causality depends on the form of f(R) and on the matter content components. We concretely examine the Gödel-type perfect-fluid solutions in the f(R) = R−fi/Rn class of Palatini gravity theories, and show that for positive matter density and for fi and n in the range permitted by the observations, these theories do not admit the Gödel geometry as a perfect-fluid solution of its field equations. In this sense, f(R) gravity theory remedies the causal pathology in the form of closed timelike curves which is allowed in General Relativity. We also examine the violation of causality of Gödel-type by considering a single scalar field as the matter content. For this source, we show that Palatini f(R) gravity gives rise to a unique Gödeltype solution with no violation of causality. Finally, we show that by combining a perfect fluid plus a scalar field as sources of Gödel-type geometries, we obtain both solutions in the form of closed time-like curves, as well as solutions with no violation of causality

Contribuição ao estudo de redes complexas: modelo de afinidade com métrica

Currently the interest in large-scale systems with a high degree of complexity has been much discussed in the scientific community in various areas of knowledge. As an example, the Internet, protein interaction, collaboration of film actors, among others. To better understand the behavior of interconnected systems, several models in the area of complex networks have been proposed. Barabási and Albert proposed a model in which the connection between the constituents of the system could dynamically and which favors older sites, reproducing a characteristic behavior in some real systems: connectivity distribution of scale invariant. However, this model neglects two factors, among others, observed in real systems: homophily and metrics. Given the importance of these two terms in the global behavior of networks, we propose in this dissertation study a dynamic model of preferential binding to three essential factors that are responsible for competition for links: (i) connectivity (the more connected sites are privileged in the choice of links) (ii) homophily (similar connections between sites are more attractive), (iii) metric (the link is favored by the proximity of the sites). Within this proposal, we analyze the behavior of the distribution of connectivity and dynamic evolution of the network are affected by the metric by A parameter that controls the importance of distance in the preferential binding) and homophily by (characteristic intrinsic site). We realized that the increased importance as the distance in the preferred connection, the connections between sites and become local connectivity distribution is characterized by a typical range. In parallel, we adjust the curves of connectivity distribution, for different values of A, the equation P(k) = P0e

Estruturas de acumulação de água subterrânea em rochas cristalinas: estudo geofísico e geológico de casos no Estado do Rio Grande do Norte

Geological and geophysical studies (resistivity, self potential and VLF) were undertaken in the Tararaca and Santa Rita farms, respectively close to the Santo Antônio and Santa Cruz villages, eastern Rio Grande do Norte State, NE Brazil. Their aim was to characterize water acummulation structures in crystalline rocks. Based on geological and geophysical data, two models were characterized, the fracture-stream and the eluvio-alluvial through, in part already described in the literature. In the Tararaca Farm, a water well was located in a NW-trending streamlet; surrounding outcrops display fractures with the same orientation. Apparent resistivity sections, accross the stream channel, confirm fracturing at depth. The VLF profiles systematically display an alignment of equivalent current density anomalies, coinciding with the stream. Based on such data, the classical fracture-stream model seems to be well characterized at this place. In the Santa Rita Farm, a NE-trending stream display a metric-thick eluvioregolith-alluvial cover. The outcropping bedrock do not present fractures paralell to the stream direction, although the latter coincides with the trend of the gneiss foliation, which dips to the south. Geophysical data confirm the absence of a fracture zone at this place, but delineate the borders of a through-shaped structure filled with sediments (alluvium and regolith). The southern border of this structure dips steeper compared to the northern one. This water acummulation structure corresponds to an alternative model as regards to the classical fracture-stream, being named as the eluvio-alluvial trough. Its local controls are the drainage and relief, coupled with the bedrock weathering preferentially following foliation planes, generating the asymmetry of the through