A discrete discontinuity between the two phases of gravity
arXiv:2210.15980 · doi:10.1088/1475-7516/2023/11/012
Abstract
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase is found to exhibit three local degrees of freedom. This reflects a discrete discontinuity in the limit of a vanishing tetrad determinant. For the particular case of vanishing lapse, the Hamiltonian constraint disappears from the classical theory upon fixing the torsional gauge-freedom. Any state functional invariant under the internal gauge rotations and spatial diffeomorphisms is a formal solution of the associated quantum theory. The formulation here provides a Hamiltonian basis to analyze gravity theory around a physical singularity, which corresponds to a zero of the tetrad determinant in curved spacetime.
15 pages, Accepted version (JCAP), Minor revisions in presentation, Title changed
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