The Poisson brackets of free null initial data for vacuum general relativity

Abstract

A hypersurface composed of two null sheets, or "light fronts", swept out by the two congruences of future null normal geodesics emerging from a spacelike 2-disk can serve as a Cauchy surface for a region of spacetime. Already in the 1960s free (unconstrained) initial data for vacuum general relativity were found for hypersurfaces of this type. Here the Poisson brackets of such free initial data are calculated from the Hilbert action. The brackets obtained can form the starting point for a constraint free canonical quantization of general relativity and may be relevant to holographic entropy bounds for vacuum gravity. Several of the results of the present work have been presented in abbreviated form in the letter [Rei08].

55 pages, 2 figures

References in corpus (6)

• Proof of a Quantum Bousso Bound
• Gravity Degrees of Freedom on a Null Surface
• First order gravity on the light front
• The Poisson bracket on free null initial data for gravity
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• Integrable structures and the quantization of free null initial data for gravity

Cited by in corpus (7)

• The Weyl BMS group and Einstein's equations
• Boundary effects in General Relativity with tetrad variables
• Quantum Null Geometry and Gravity
• Generating functional for gravitational null initial data
• Gravitational Constraints on a Lightlike boundary
• Evidence for Planck Luminosity Bound in Quantum Gravity
• Gravitational null rays: Covariant Quantization and the Dressing Time