First order gravity on the light front

TL;DR

This paper explores the canonical structure of first order general relativity on a null foliation, revealing unique constraint features and providing a framework for addressing zero modes relevant to quantum gravity approaches.

Contribution

It introduces a tetrad-based formalism for null foliations in first order gravity, highlighting the nature of constraints and zero modes, aiding quantum gravity quantization.

Findings

Dynamical Einstein equations appear as second class tertiary constraints.

Framework for analyzing zero modes in gravity.

Insights applicable to loop quantum gravity and spin foam models.

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 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.