Abstract
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 necessary between the brane tensions and the bulk cosmological constant. By further relaxing the sole fine-tuning of the model, we derive nonstatic solutions, describing de Sitter or anti–de Sitter 4-dimensional spacetimes, that 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 employing small, time-dependent perturbations around the background solutions. In analogy with results drawn in five dimensions, the solutions describing a de Sitter 4-dimensional spacetime turn out to be unstable while those describing an anti–de Sitter geometry are shown to be stable.
- Received 24 April 2001
DOI:https://doi.org/10.1103/PhysRevD.64.044021
©2001 American Physical Society