Generalized embedding variables for geometrodynamics and space-time diffeomorphisms: Ultralocal coordinate conditions

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Abstract
The embedding variable approach to geometrodynamics advocated in work by Isham, Kuchař, and Unruh are investigated for a general class of coordinate conditions that mirror the Isham–Kuchař Gaussian condition, but allow for arbitrary algebraic complexity. It is found that the same essential structure present in the ultralocal Gaussian condition is repeated in the general case. The resultant embedding-extended phase space contains a full representation of the Lie algebra of the space-time diffeomorphism group, as well as a consistent pure gravity sector.
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