Abstract
When tetrad (metric) fields are not invertible, the standard canonical formulation ofgravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity fornoninvertible tetrad. In contrast to Einstein gravity, this phase is found to exhibit threelocal degrees of freedom. This reflects a discrete discontinuity in the limit of a vanishingtetrad determinant. For the particular case of vanishing lapse, the Hamiltonian constraintdisappears from the classical theory upon fixing the torsional gauge-freedom. Any statefunctional invariant under the internal gauge rotations and spatial diffeomorphisms is a formal solution of the associated quantum theory. The formulation here provides a Hamiltonianbasis to analyze gravity theory around a physical singularity, which corresponds to a zero ofthe tetrad determinant in curved spacetime.
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