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 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.

35 pages, 1 figure; minor corrections, added references

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Cited by in corpus (17)

• Boundary effects in General Relativity with tetrad variables
• A gauge-invariant symplectic potential for tetrad general relativity
• Stress Tensor on Null Boundaries
• Sachs' free data in real connection variables
• Canonical analysis of Holst action without second-class constraints
• The Poisson brackets of free null initial data for vacuum general relativity
• Gravity as an SU(1,1) gauge theory in four dimensions
• Kac-Moody symmetry in the light front of gauge theories
• Spinfoams: Foundations
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Bi-gravity with a single graviton
• Constrained gauge-gravity duality in three and four dimensions
• Canonical structure of minimal varying $\Lambda$ theories
• Gravitational Constraints on a Lightlike boundary
• Hamiltonian Analysis of 3-dimensional Spacetime in Bondi-like Coordinates
• Phase space for gravity with boundaries
• Dynamical Structure of the Fields in the Light Cone Coordinates