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The unique ghost-free mass and nonlinear potential terms for generalrelativity are presented in a diffeomorphism and local Lorentz invariantvierbein formalism. This construction requires an additional two-indexStuckelberg field, beyond the four scalar fields used in the metricformulation, and unveils a new local SL(4) symmetry group of the mass andpotential terms, not shared by the Einstein-Hilbert term. The new field isauxiliary but transforms as a vector under two different Lorentz groups, one ofthem the group of local Lorentz transformations, the other an additional globalgroup. This formulation enables a geometric interpretation of the mass andpotential terms for gravity in terms of certain volume forms. Furthermore, wefind that the decoupling limit is much simpler to extract in this approach; inparticular, we are able to derive expressions for the interactions of thevector modes. We also note that it is possible to extend the theory bypromoting the two-index auxiliary field into a Nambu-Goldstone bosonnonlinearly realizing a certain space-time symmetry, and show how it is "eatenup" by the antisymmetric part of the vierbein.

On the Potential for General Relativity and its Geometry