Soluções exatas com simetria axial na relatividade geral: um estudo sobre estrelas em modelos de branas.

Abstract

I n the context of extra dimensional theories, the braneworld RSII model has attracted much interest. According to this model, our universe is a four-dimensional hypersurface embedded i n an ambient space w i t h a non-compact extra dimension and a negative cosmological constant. A great challenge for the model, and i n general, for the General Relativity Theory, is to find exact solutions w i t h clear physical interpretation. I n this work, we intend to obtain exact solutions of Einstein's equations related t o stars confined to the brane i n the RSII model. I n five dimensions, the system composed by the brane and by the confined star possesses axial symmetry. Despite the symmetry, the direct resolution of the Einstein equations for this system is a very difficult task. Therefore, in order to obtain the solutions we have to use the alternative method known as "displace, cut and reflect". This method consists of dividing a space already known ( in our case, the Schwarzschild-AdSs space-time) into two parts by a cut i n a plane located above the source (z = c > 0, i n the Weyl coordinates). The b o t t om part, which contains the source, is eliminated and replaced by the reflected image of the upper region. The new space-time that arises by this procedure presents a discontinuity in the plane of the cut, therefore, indicating the presence of matter concentrated at that hypersurface. From the Einstein's equations, we can determine the density and pressure of the matter d i s t r i b u t i on which was obtained. Examining these quantities, we find that, besides the energy content of the brane itself, there is a body w i t h spherical symmetry (the star confined on the brane). Employing the embedding formalism, more general cuts, which are not limited to planes, may be considered. In all cases examined, the body has positive energy density. However, there are regions where the dominant energy condition is not fulfilled, i.e., where the pressure is greater than the energy density.