On a class of 2-surface observables in general relativity
arXiv:gr-qc/0511059 · doi:10.1088/0264-9381/23/7/006
Abstract
The boundary conditions for canonical vacuum general relativity is investigated at the quasi-local level. It is shown that fixing the area element on the 2- surface S (rather than the induced 2-metric) is enough to have a well defined constraint algebra, and a well defined Poisson algebra of basic Hamiltonians parameterized by shifts that are tangent to and divergence-free on $. The evolution equations preserve these boundary conditions and the value of the basic Hamiltonian gives 2+2 covariant, gauge-invariant 2-surface observables. The meaning of these observables is also discussed.
11 pages, a discussion of the observables in stationary spacetimes is included, new references are added, typos corrected
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- Report on GRG18, Session A3, Mathematical Studies of the Field Equations