Five-dimensional cosmological models in induced matter theory

Abstract

A class of five-dimensional space–times that contain four-dimensional hypersurfaces whose intrinsic metrics are Friedman–Robertson–Walker (FRW) metrics is examined (the four-dimensional intrinsic Lorentzian metrics are both spatially homogeneous and isotropic). The five-dimensional vacuum field equations, 5Gij=0, are shown to induce four-dimensional perfect-fluid FRW field equations, 4Gij=4Tij, and thus these FRW cosmological models may be interpreted as being purely geometrical in origin.