  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 analyse 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.
