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

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

2005-11-02

arxiv.org/abs/gr-qc/0511012v1

J.Math.Phys. 46 (2005) 102501

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages

Scientific paper

10.1063/1.2042968

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.

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