The embedding of General Relativity in five dimensions

Details The embedding of General Relativity in five dimensions The embedding of General Relativity in five dimensions

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gregr..28..365r&link_type=abstract

General Relativity and Gravitation, Volume 28, Issue 3, pp.365-376

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79

Scientific paper

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.

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