On new variational principles as alternatives to the Palatini method

Understand

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.