  We study the canonical structure of the real first order formulation of
general relativity on a null foliation. We use a tetrad decomposition which
allows to elegantly encode the nature of the foliation in the norm of a vector
in the fibre bundle. The resulting constraint structure shows some
peculiarities. In particular, the dynamical Einstein equations propagating the
physical degrees of freedom appear in this formalism as second class tertiary
constraints, which puts them on the same footing as the Hamiltonian constraint
of the Ashtekar's connection formulation. We also provide a framework to
address the issue of zero modes in gravity, in particular, to study the
non-perturbative fate of the zero modes of the linearized theory. Our results
give a new angle on the dynamics of general relativity and can be used to
quantize null hypersurfaces in the formalism of loop quantum gravity or spin
foams.
