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On a class of 2-surface observables in general relativity

The boundary conditions for canonical vacuum general relativity are investigated at the quasi-local level. It is shown that fixing the area element on the 2-surface (rather than the induced 2-metric) is enough to have a well-defined constraint algebra, and a well-defined Poisson algebra of basic Hamiltonians parametrized by shifts that are tangent to and divergence free on . The evolution equations preserve these boundary conditions, and the value of the basic Hamiltonians gives 2+2-covariant, gauge-invariant 2-surface observables. The meaning of these observables is also discussed.