New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in
  Vielbein Form
  We reconsider the possibility of a class of new kinetic terms in the first
order (vielbein) formulation of massive gravity and multi-gravity. We find that
new degrees of freedom emerge which are not associated with the Boulware--Deser
ghost and are intrinsic to the vielbein formulation. These new degrees of
freedom are associated with the Lorentz transformations which encode the
additional variables contained in the vielbein over the metric. Although they
are not guaranteed to be ghostly, they are nevertheless infinitely strongly
coupled on Minkowski spacetime and are not part of the spin-2 multiplet. Hence
their existence implies the uniqueness of the Einstein--Hilbert term as the
kinetic term for a massive graviton.
