The approach to gravity as a theory of embedded surface

Abstract

We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function. The Euler-Lagrange equations for this theory (Regge-Teitelboim equations) are more general than the Einstein equations, and admit "extra solutions" which do not correspond to any Einsteinian metric. The Regge-Teitelboim equations can be explicitly analyzed for the solutions with high symmetry. We show that symmetric embeddings of a static spherically symmetric asymptotically flat metrics in a 6-dimensional ambient space do not admit extra solutions of the vacuum Regge-Teitelboim equations. Therefore in the embedding theory the solutions with such properties correspond to the exterior Schwarzchild metric.

LaTeX, 10 pages. Proceedings of "II Russian-Spanish Congress Particle and Nuclear Physics at all Scales and Cosmology", Saint-Petersburg, October 1-4, 2013

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• 3+1 decomposition in the new action for the Einstein Theory of Gravitation
• New action for the Hilbert-Einstein equations
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