A review of six-dimensional braneworld solutions /

In the last years, brane world scenarios have been studied extensively, but most of these studies have been done in the case of five-dimensional spacetime. It is therefore of interest to investigate which of the particular features observed are proper to one extra dimension and which are generic to any number of dimensions. In this thesis, I present an overview of models and solutions to Einstein's equations for six-dimensional brane world scenarios. Solutions for a simple setup with cylindrically symmetric bulk centered about a three-brane are derived and classified. There are two main kinds of topology: either solutions are compactified in a spherical topology, closed up by another three-brane, or they have a disc topology, which must be terminated by a four-brane. One of the particular features of codimension-two branes is demonstrated, namely that their tension, or vacuum energy, induces a deficit angle in the bulk. Solutions for different arrangements of codimension-one and codimension-two branes are also reviewed. Although the review focuses on topological and cosmological properties of the solutions, models using a field theoretical approach to the brane-world scenario, i.e. considering the brane as a topological defect arising from higher dimensional fields, are also considered