The initial boundary value problem and quasi-local Hamiltonians in general relativity

We discuss relations between the initial boundary value problem (IBVP) and quasi-local Hamiltonians in GR. The latter have traditionally been based on Dirichlet boundary conditions, which however are shown here to be ill-posed for the IBVP. We present and analyze several other choices of boundary conditions which are better behaved with respect to the IBVP and carry out a corresponding Hamiltonian analysis, using the framework of the covariant phase space method.

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