Soluções cosmológicas e locais para uma eletrodinâmica modificada

The present work investigates some consequences that arise from the use of a modifed lagrangean for the eletromagnetic feld in two diferent contexts: a spatially homogeneous and isotropic universe whose dynamics is driven by a magnetic feld plus a cosmological parameter A, and the problem of a static and charged point mass (charged black hole). In the cosmological case, three diferent general solutions were derived. The first, with a null cosmological parameter A, generalizes a particular solution obtained by Novello et al [gr-qc/9806076]. The second one admits a constant A and the third one allows A to be a time-dependent parameter that sustains a constant magnetic feld. The first two solutions are non-singular and exhibit in ationary periods. The third case studied shows an in ationary dynamics except for a short period of time. As for the problem of a charged point mass, the solutions of the Einstein-Maxwell equations are obtained and compared with the standard Reissner-Nordstrom solution. Contrary to what happens in the cosmological case, the physical singularity is not removed

Setor escuro do universo: uma análise termodinâmica

Significant observational effort has been directed to unveiling the nature of the so-called dark energy. However, given the large number of theoretical possibilities, it is possible that this a task cannot be based only on observational data. In this thesis we investigate the dark energy via a thermodynamics approach, i.e., we discuss some thermodynamic properties of this energy component assuming a general time-dependent equation-of-state (EoS) parameter w(a) = w0 + waf(a), where w0 and wa are constants and f(a) may assume different forms. We show that very restrictive bounds can be placed on the w0 - wa space when current observational data are combined with the thermodynamic constraints derived. Moreover, we include a non-zero chemical potential μ and a varying EoS parameter of the type ω(a) = ω0 + F(a), therefore more general, in this thermodynamical description. We derive generalized expressions for the entropy density and chemical potential, noting that the dark energy temperature T and μ evolve in the same way in the course of the cosmic expansion. The positiveness of entropy S is used to impose thermodynamic bounds on the EoS parameter ω(a). In particular, we find that a phantom-like behavior ω(a) < −1 is allowed only when the chemical potential is a negative quantity (μ < 0). Thermodynamically speaking, a complete treatment has been proposed, when we address the interaction between matter and energy dark

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time