Bubble dynamics and spontaneous compactification

As a laboratory for studying dimensional reduction in inhomogeneous spacetimes, we consider several five-dimensional models in which a bubble of a spacetime with a small compact dimension is sewn to a spacetime with all five dimensions macroscopic. Obliging the five-dimensional metric to be well behaved at the domain boundary constrains the parameters of the composite spacetimes under study. Given a suitable potential, it is possible that the domain wall is created by the rapid variation of the size of the compact dimension. Then it is appropriate to reduce the five-dimensional theory to an effective four-dimensional theory in which the size of the compact dimension plays the role of a scalar field. It is the effective four-dimensional metric which must be well defined at the domain boundary. We discuss several models of this latter type including some in which there is no singular contribution to the effective energy-momentum tensor even at the domain boundary.