The embedding of space-times in five dimensions with nondegenerate Ricci tensor

We discuss and prove a theorem which asserts that any n-dimensional semi-Riemannian manifold can be locally embedded in an (n+1)-dimensional space with a nondegenerate Ricci tensor which is equal, up to a local analytic diffeomorphism, to the Ricci tensor of an arbitrary specified space. This may be regarded as a further extension of the Campbell-Magaard theorem. We highlight the significance of embedding theorems of increasing degrees of generality in the context of higher dimensional space-times theories and illustrate the new theorem by establishing the embedding of a general class of Ricci-flat space-times. (C) 2002 American Institute of Physics.