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

TL;DR

This paper calculates the Poisson brackets of free null initial data on a hypersurface composed of two light fronts in vacuum general relativity, providing a basis for canonical quantization and holographic entropy considerations.

Contribution

It derives the Poisson brackets for free null initial data in vacuum GR from the Hilbert action, enabling constraint-free canonical quantization.

Findings

Poisson brackets for null initial data are explicitly calculated.

Results facilitate potential canonical quantization of vacuum GR.

Findings may impact holographic entropy bounds in gravity.

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].