6-dimensional brane world model - art. no. 044021

We consider a 6-dimensional spacetime which is periodic in one of the extra dimensions and compact in the other. The periodic direction is defined by two 4-brane boundaries. Both static and nonstatic exact solutions, in which the internal spacetime has a constant radius of curvature, are derived. In the case of static solutions, the brane tensions must be tuned as in the 5 -dimensional Randall-Sundrum model; however, no additional fine-tuning is n ecessary between the brane tensions and the bulk cosmological constant. By further relaxing the sole fine-tuning of the model, we derive nonstatic sol utions, describing de Sitter or anti-de Sitter 4-dimensional spacetimes. th at allow for the fixing of the interbrane distance and the accommodation of pairs of positive-negative and positive-positive tension branes. Finally, we consider the stability of the radion field in these configurations by em ploying small, time-dependent perturbations around the background solutions . In analogy with results drawn in five dimensions. the solutions describin g a de Sitter 4-dimensional spacetime turn out to be unstable while those d escribing an anti-de Sitter geometry are shown to be stable.