The dynamics of strong coupling gravity

Abstract

In the limit of infinite Newton constant, the dimensional vacuum Einstein equations reduce to their ‘velocity dominated’ counterparts. We construct all solutions with generic initial data and spatially closed sections by employing the constant mean curvature (CMC) gauge []. The latter is a nonlinearly admissible gauge in which the evolution equations are integrable ordinary differential equations and the diffeomorphism constraint decouples from the Hamiltonian constraint. The dynamical fields in this gauge are invariant under all gauge transformations but time independent spatial diffeomorphisms. The decoupled constraints are solved using a lapse-weighted conformal-traceless decomposition and produce equivalence classes of physical configurations modulo spatial diffeomorphisms. The CMC gauge can be augmented by a gauge condition on the unimodular part of the spatial metric to provide a complete gauge fixing. Based on it a complete set of fully gauge invariant dynamical fields (observables) is constructed. By utilizing an algebraic gauge condition a variant of the construction is found that isolates the physical degrees of freedoms algebraically.