First order gravity on the light front

Abstract

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 us to elegantly encode the nature of the foliation in the norm of a vector in the fiber 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 Ashtekar's connection formulation. We also provide a framework to address the issue of zero modes in gravity, in particular, to study the nonperturbative 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.