A hypersurface-anchored variational principle supplements the Einstein-Hilbert action with a functional on a varied spacelike hypersurface, yielding standard bulk equations plus distributional contributions and an anchoring condition that selects admissible embeddings.
Role of surface integrals in hamiltonian formulation of general relativity.Annals of Physics, 88:286–318, 1974
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Hypersurface Anchored Variational Principle for General Relativity
A hypersurface-anchored variational principle supplements the Einstein-Hilbert action with a functional on a varied spacelike hypersurface, yielding standard bulk equations plus distributional contributions and an anchoring condition that selects admissible embeddings.