6-dimensional brane world model

We consider a 6D space-time which is periodic in one of the extra dimensionsand compact in the other. The periodic direction is defined by two 4-braneboundaries. Both static and non-static exact solutions, in which the internalspacetime has constant radius of curvature, are derived. In the case of staticsolutions, the brane tensions must be tuned as in the 5D Randall-Sundrum model,however, no additional fine-tuning is necessary between the brane tensions andthe bulk cosmological constant. By further relaxing the sole fine-tuning of themodel, we derive non-static solutions, describing de Sitter or Anti de Sitter4D spacetimes, that allow for the fixing of the inter-brane distance and theaccommodation of pairs of positive-negative and positive-positive tensionbranes. Finally, we consider the stability of the radion field in theseconfigurations by employing small, time-dependent perturbations around thebackground solutions. In analogy with results drawn in 5 dimensions, thesolutions describing a de Sitter 4D spacetime turn out to be unstable whilethose describing an Anti de Sitter geometry are shown to be stable.Comment: 22 pages, LaTeX file, no figure