The Poisson bracket on free null initial data for gravity

Abstract

Free initial data for general relativity on a pair of intersecting null hypersurfaces are well known, but the lack of a Poisson bracket and concerns about caustics have stymied the development of a constraint free canonical theory. Here it is pointed out how caustics and generator crossings can be neatly avoided and a Poisson bracket on free data is given. On sufficiently regular functions of the solution spacetime geometry this bracket matches the Poisson bracket defined on such functions by the Hilbert action via Peierls' prescription. The symplectic form is also given in terms of free data.

4 pages,1 figure. Some changes to text to improve clarity of presentation, this is the final published version

References in corpus (5)

• The World as a Hologram
• A Covariant Entropy Conjecture
• Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• The symplectic 2-form and Poisson bracket of null canonical gravity

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• The Weyl BMS group and Einstein's equations
• Time evolution as refining, coarse graining and entangling
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• Quantum Null Geometry and Gravity
• The symplectic 2-form for gravity in terms of free null initial data
• Sachs' free data in real connection variables
• The Poisson brackets of free null initial data for vacuum general relativity
• Integrable structures and the quantization of free null initial data for gravity
• Asymptotic Limit of Null Hypersurfaces