The Poisson bracket on free null initial data for gravity.
Free initial data for general relativity on a pair of intersecting null hypersurfaces are well known, but the lack of Poisson brackets 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 Poisson brackets on free data are given. On sufficiently regular functions of the solution spacetime geometry these brackets match the Poisson brackets defined on such functions by the Hilbert action via Peierls' prescription. The symplectic 2-form is also given in terms of free data.
Reisenberger
Michael P
MP
Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400 Montevideo, Uruguay.