Spherically symmetric wormholes of embedding class one

Abstract

This paper generalises an earlier result by the author based on the well-established embedding theorems that connect the classical theory of relativity to higher-dimensional space–times. In particular, an n-dimensional Riemannian space is said to be of class m if $m+n$ is the lowest dimension of the flat space in which the given space can be embedded. To study traversable wormholes, we concentrate on spacetimes that can be reduced to embedding class one by a suitable transformation. It is subsequently shown that the extra degrees of freedom from the embedding theory provide the basis for a complete wormhole solution in the sense of obtaining both the redshift and shape functions.