Speaker
Description
We address the problem of setting up a Hamiltonian theory of gravity when the tetrad (metric) fields are not invertible. We find that this theory exhibits three local degrees of freedom, thus revealing that the limit to a vanishing tetrad determinant is discretely discontinuous. This outcome is shown to be independent of whether the null eigenvalue of the four-metric lies along a timelike or a spacelike direction. For the particular case of vanishing lapse, the Hamiltonian constraint could be made to disappear from the canonical theory by 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 gravity theory. The framework here could provide a Hamiltonian basis to analyze a physical singularity when it is associated with a degenerate tetrad everywhere, as in the case of the Belinski-Khalatnikov-Lifshitz behaviour in cosmology.
