Simpler Hamiltonian structure of Gravity in degenerate limit

Abstract: We analyze Hamiltonian gravity in the limit of a vanishing (spatial) triad determinant. In the context of Barbero-Immirzi formulation, the Lorentzian constraints in this limit are found to exhibit a formal similarity to the Euclidean constraints of Ashtekar's self-dual formulation, modulo the difference that the spatial diffeomorphisms become trivial. Further, we show that the Carrollian limit of gravity emerges as a special case, thus providing it a geometric interpretation independent of either the speed of light or coupling constants.