  We show that the Hamiltonian form of gravity in terms of connection and
densitized triad variables admits a simpler structure close to a (spacelike)
curvature singularity. To define this regime, we construct a limit to a
vanishing (spatial) metric determinant. The cosmological and black hole
spacetime solutions that characterize such an approach to a singularity are
obtained. We also elucidate the connection of this generic limit to the
`Carroll' limit which could be interpreted as a special case.
