Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares

The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Arquitetura, litofácies e evolução tectonoestratigráfica da bacia do rio do peixe, nordeste do Brasil

The Rio do Peixe Basin is located in the border of Paraíba and Ceará states, immediately to the north of the Patos shear zone, encompassing an area of 1,315 km2. This is one of the main basins of eocretaceous age in Northeast Brazil, associated to the rifting event that shaped the present continental margin. The basin can be divided into four sub-basins, corresponding to Pombal, Sousa, Brejo das Freiras and Icozinho half-grabens. This dissertation was based on the analysis and interpretation of remote sensing products, field stratigraphic and structural data, and seismic sections and gravity data. Field work detailed the lithofacies characterization of the three formations previously recognised in the basin, Antenor Navarro, Sousa and Rio Piranhas. Unlike the classical vertical stacking, field relations and seismostratigraphic analysis highlighted the interdigitation and lateral equivalency between these units. On bio/chrono-stratigraphic and tectonic grounds, they correlate with the Rift Tectonosequence of neocomian age. The Antenor Navarro Formation rests overlies the crystalline basement in non conformity. It comprises lithofacies originated by a braided fluvial system system, dominated by immature, coarse and conglomeratic sandstones, and polymict conglomerates at the base. Its exposures occur in the different halfgrabens, along its flexural margins. Paleocurrent data indicate source areas in the basement to the north/NW, or input along strike ramps. The Sousa Formation is composed by fine-grained sandstones, siltites and reddish, locally grey-greenish to reddish laminated shales presenting wavy marks, mudcracks and, sometimes, carbonate beds. This formation shows major influence of a fluvial, floodplain system, with seismostratigraphic evidence of lacustrine facies at subsurface. Its distribution occupies the central part of the Sousa and Brejo das Freiras half-grabens, which constitute the main depocenters of the basin. Paleocurrent analysis shows that sediment transport was also from north/NW to south/SE