Abstract We construct a limit of Hamiltonian gravity as the determinant of the spatial triad (and henceof the four-metric) goes to zero. Within the Barbero-Immirzi SU (2) formulation, we present twopossible realizations of this limit, with the consequence that the Hamiltonian constraint becomessimpler and spatial diffeomorphisms become trivial. In the first case, the Hamiltonian constraintexhibits a polynomial structure, being formally similar to the Euclidean Hamitonian constraintof Sen-Ashtekar self-dual formulation. In the latter, the constraints become free from orderingambiguity. Further, we show that the Carrollian gravity emerges as a special case of this degeneratelimit, thus providing it a new geometric interpretation independent of the speed of light or anydimensionful coupling constant (G).
Sandipan Sengupta (2025) studied this question.