**Authors**: Frank B. Estabrook

**Date**: 3 Aug 2009

**Abstract**: We formulate, and solve in several symmetric cases, the classical field-theoretic dynamics that arises when the Hilbert-Einstein Lagrangian is taken as the action for isometric embedding of 4-spaces into ten flat dimensions. Its variation gives the Euler-Lagrange equations of a well- posed multicontact field theory. The Hilbert Lagrangian as usually varied over just the intrinsic curvature structure of a 4-space yields only a subset of this dynamics, viz., solutions whose initial conditions constrain them to be Ricci-flat. We conjecture that there may be a classical correspondence with the hidden dimensions of brane theory, and that perhaps this extended general relativistic dynamics holds in extreme circumstances where it can be interpreted as including a sort of dark energy, although no term with a cosmological constant is included in the Lagrangian. As a multicontact system, canonical quantization should be straightforward.

0908.0365
(/preprints)

2009-08-06, 08:33
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*