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

Harry I. Ringermacher·Lawrence R. Mead
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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.

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Harry I. Ringermacher, Lawrence R. Mead. 2005-11-02. Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space. https://doi.org/10.1063/1.2042968

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