The Poisson bracket on free null initial data for gravity

Details The Poisson bracket on free null initial data for gravity The Poisson bracket on free null initial data for gravity

2007-12-15

arxiv.org/abs/0712.2541v4

Phys.Rev.Lett.101:211101,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevLett.101.211101

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.

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