Plane domain walls when coupled with the Brans-Dicke scalar field.

Abstract

The space-times of plane thin domain walls are studied in the context of the Brans-Dicke (BD) theory of gravity by using distribution theory. In particular, the BD field equations are divided into two groups: one holding in the regions outside of the wall and the other holding on the wall. It is found that the equations on the wall take a very simple form, and are given explicitly in terms of the metric coefficients and the BD scalar field. As an application of the theory developed, a class of exact solutions, which represents a plane domain wall interacting with the BD scalar field, is given and studied. It is found that the surface energy density of the wall always exponentially decreases as the time develops; this is one possible solution of the domain wall problem in cosmological models founded on general relativity. The space-time is usually singular not only at the initial point, but also at spacelike infinity. However, the proper distance from the wall to the singularities at spacelike infinity is finite but exponentially increasing (in fact, inversely proportional to the surface energy density of the wall).