Equivalence between Palatini and metric formalisms of f(R)-gravity by
  divergence free current
  The equivalence between metric and Palatini formalisms in f(R)-gravity can be
achieved in the general context of theories with divergence free current. This
equivalence is a necessary result of a symmetry which is included in a
particular conservation equation of the current. In fact the conservation
equation, by an appropriate redefinition of the introduced auxiliary field, may
be encoded in a massless scalar field equation.
