On new variational principles as alternatives to the Palatini method

TL;DR

This paper explores alternative variational principles to the Palatini method, revealing their equivalence or physical distinction through bimetric reformulations and connections to C-theories.

Contribution

It demonstrates that certain variational principles are equivalent to Palatini, while introducing new bimetric formulations that differ physically, expanding the landscape of gravitational theories.

Findings

Palatini equivalence of Goenner's variational principle

Bimetric reformulation yields physically distinct theories

Connections to decoupling limits of C-theories

Abstract

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.