Induced matter theory and embeddings in Riemann flat space–times

Abstract

A class of five-dimensional space-times that contain four-dimensional hypersurfaces whose intrinsic metrics are of cosmological interest is investigated. First, the five-dimensional space–time is assumed to be Riemann flat—the problem of determining the intrinsic metrics of the four-dimensional hypersurfaces then becomes a problem of embedding in flat space–time. Second, the Riemann flat solutions are used as a starting point to find solutions to Einstein’s vacuum field equations in five dimensions that are not Riemann flat. In particular, a new general class of five-dimensional vacuum solutions is found.