Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

TL;DR

This paper generalizes the concept of induced matter in higher-dimensional spaces, showing that N-dimensional curved manifolds can be embedded in Riemann-flat N+1-dimensional spaces, which induce matter purely through geometry.

Contribution

It provides a general theorem describing how N-dimensional maximally symmetric spaces can be embedded in Riemann-flat N+1-dimensional manifolds, extending previous specific solutions.

Findings

N-manifolds can be any maximally symmetric space

Embedded N-manifolds are solutions of Einstein equations

Induced matter arises from geometric structure

Abstract

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.