Invariant Foliation of Dynamical Spacetimes

We present a gauge-theoretical derivation of the Frobenius foliation condition. It is based on a nonlinear coset realization of the Poincaré group, implying the time component ⁰ of the coframe to be invariant. By means of the unitary gauge fixing of the boosts, three Goldstone-like degrees of freedom of ⁰ are eliminated. The remaining Higgs-like boson, satisfying the foliation condition, plays the role of time.