On new variational principles as alternatives to the Palatini method
  A variational principle was recently suggested by Goenner, where an
independent metric generates the spacetime connection. It is pointed out here
that the resulting theory is equivalent to the usual Palatini theory. However,
a bimetric reformulation of the variational principle leads to theories which
are physically distinct from both the metric and the metric-affine ones, even
for the Einstein-Hilbert action. They are obtained at a decoupling limit of
C-theories, which contain also other viable generalizations of the Palatini
theories.
