Time Evolution in Dynamical Spacetimes

Abstract

We present a gauge--theoretical derivation of the notion of time, suitable to describe the Hamiltonian time evolution of gravitational systems. It is based on a nonlinear coset realization of the Poincar\'e group, implying the time component of the coframe to be invariant, and thus to represent a metric time. The unitary gauge fixing of the boosts gives rise to the foliation of spacetime along the time direction. The three supressed degrees of freedom correspond to Goldstone--like fields, whereas the remaining time component is a Higgs--like boson.