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.
Singular hypersurfaces and thin shells in general relativity.Il Nuovo Cimento B (1965-1970), 44:1–14, 1966
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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.