Defeitos topológicos e uma solução tipo-Schwarzschild num modelo bumblebee de gravitação

Abstract

The Thesis is divided in two parts. In the first one, we show the existence of self-dual solutions obtained in two distinct contexts: BPS vortices in new Maxwell-Higgs scenarios with k-generalized dynamic and electrically charged Skyrmions BPS. In both cases, we implement consistently the BPS formalism, obtaining the respective self-dual equations which describe the topological structures in each context. The BPS vortices engendered in the k-generalized models are electrically neutral, possessing total energy proportional to the magnetic flux; the numerical solutions show that the generalization modifies the vortex core size, the magnetic field amplitudes and the bosonic mass, holding the total energy proportional to the topologically quantized magnetic flux. The Skyrmions BPS are obtained from the well-known gauged baby Skyrme model whose gauge field now is also governed by the Chern-Simons term; the presence of the Chern-Simons action allows the existence of electrically charged self-dual solitons possessing magnetic flux, too. The numerical solutions of the Skyrmions BPS show that the choice of the superpotential has a direct effect on the behavior of these structures, being able to have an exponential decay or a power-law decay. In the second part of this work, we get an exact Schwarzschild-like solution in a bumblebee gravity model which is contained in the minimal standard-model extension. The theoretical model assumes a coupling of the bumble bee field to a Riemaniann space-time, this field being responsible by the effects of the spontaneous Lorentz symmetry breaking. The solution is obtained in a static and spherically symmetric scenario, thus establishing what we can call of modified black hole solution or Schwarzschild-like solution. We have investigated upper-bounds for Lorentz violation from the experimental data obtained for some classic tests of General Relativity; between these tests we restrict our attention to the advance of perihelion of inner planets, the bending of light and the time delay effect. Among actual obser ved data, the estimates found for the Lorentz violating parameter has achieved 10−15 level. Among experiments developed with some future projections of results, it is possible to obtain a sensitivity reaching the 10−19 level.