The Poisson bracket on free null initial data for gravity

Understand

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.