The gauge structure of strong coupling gravity

In the limit of infinite Newton constant the dimensional Einstein–Hilbert action reduces to that of a nonlinear sigma-model where spatial points are coupled merely by shift terms giving rise to a diffeomorphism constraint. The full group of diffeomorphisms is shown to act non-tensorially as a gauge group on the action and the field equations. This is used to establish the admissibility as a gauge condition of the combined constant mean curvature (CMC) and zero shift conditions for spatially closed hypersurfaces. This 'CMC gauge' eventually allows for a concise isolation of the gauge invariant and physical degrees of freedoms. Here we utilize the CMC gauge to obtain a complete set of dynamical fields which are invariant under all gauge transformations but time independent spatial diffeomorphisms.