Generalized embedding variables for geometrodynamics and spacetime diffeomorphisms: Ultralocal coordinate conditions

Abstract

We investigate the embedding variable approach to geometrodynamics advocated in work by Isham, Kuchař and Unruh for a general class of coordinate conditions that mirror the Isham-Kuchař Gaussian condition but allow for arbitrary algebraic complexity. We find 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 spacetime diffeomorphism group as well as a consistent pure gravity sector.