Gravidade (2+1)-dimensional: um laboratório teórico para alguns dos desafios da relatividade geral

• Main Author: Martins, Marina Reis
• Publication Date: 2009
• Format: Doctoral thesis
• Language: por
• Source: Biblioteca Digital de Teses e Dissertações da UERJ
• Download full: http://www.bdtd.uerj.br/handle/1/12867
• topic: Inhomogeneity; Phantom energy; Naked singularity; Black hole; Collapse gravitational; Não-homogeneidade; Energia fantasma; Singularidade Nua; Buraco Negro; Colapso Gravitacional; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL::RELATIVIDADE E GRAVITACAO

The phenomenon of gravitational collapse and the structure of relativistic stars is of great importance in astrophysics since the formulation of general relativity. Some more recent works has revealed important advances in our understanding of the structures formation, as black holes and naked singularities and of exotic behavior fluids, as dark matter, dark energy, including here, phantom fluids. The complexity of the gravitational collapse study is related with the relatively few analytic solutions available for study. Recently, self-similar solutions of the Einstein's field equations have attracted a great deal of attention, not only because they can be studied analytically through simplification of the problem, but also because of their relevance in astrophysics. In this work, we study the gravitational collapse of the anisotropic fluid with selfsimilarity of the second and first kinds in (2+1)-dimensional spacetimes with circular symmetry. By imposing the equations of state pr = 0 and pθ = ωρ, where ρ denotes the energy density, pr and pθ the pressures in the radial and tangential direction of the fluid, we show that, for the solutions with self-similarity of the second kind, exists two distinct families. For one of the families, the only allowed solutions are the ones that represent dust fluid. All such solutions to the Einstein's field equations are found and their local and global properties are studied in detail. It is found that some can be interpreted as representing gravitational collapse, in which both naked singularities and black holes can be formed. For the other family of solutions, we have an cosmological model with accelerated expansion, which begins in a initial singularity (t = 0), with all the energy conditions satisfied. Our proposal was to investigate the hole of the inhomogeneity on the fluid's acceleration. In order to study the solutions with self-similarity of the first kind, we showed that there is a solution which represents a gravitational collapse process, resulting in a final structure of black hole or naked singularity, which can be constituted by normal or phantom fluid.