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Hypersurfaces of Five Dimensional Space-times

M. D. Maia
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Abstract

It is shown that a space-time hypersurface of a 5-dimensional Ricci-flat space-time has its energy momentum tensor algebrically related to its extrinsic curvature and to the Riemann curvature of the embedding space. It is also seen that the Einstein-Maxwell field does not arise naturally from this geometry, so that a Kaluza-Klein model based on it would require further assumptions.

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M. D. Maia. 1996-09-19. Hypersurfaces of Five Dimensional Space-times. https://arxiv.org/abs/gr-qc/9512002

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