Spacetime compactification induced by scalar fields

Abstract

This thesis work is devoted to a discussion of spacetime compactification via scalar fields. We first provide an introduction to basic concepts and mecanisms, and review existing compactification methods. We then review and discuss spacetime compactification triggered by non-linear sigma model fields. We study spacetime compactification via a single scalar field by requiring scalar field in higher dimensions to gravitate only in a subset of dimensions. For this purpose we first review fully non-gravitating scalar field configurations and then determine conditions and mecanisms for obtaining a partially gravitating scalar field. In each case Ricci and hence energy-momentum tensor of the scalar field vanishes completely or partially though this does not imply or reqire scalar field itself to vanish. By making use of the partially-gravitating scalar fields, we discuss how spacetime dimensions get compactified if the scalar field gravitates in those dimensions, only. We illustrate how this mechanism works in special cases, like generating a constant-curvature manifold of extra dimensions.