Universality of the Einstein theory of gravitation

Abstract

We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian [Formula: see text] by a generic scalar density [Formula: see text] depending upon the metric [Formula: see text] and the curvature tensor [Formula: see text], are equivalent to the conventional Einstein theory for a (possibly) different metric tensor [Formula: see text] and (possibly) a different set of matter fields. The simple proof of this theorem relies on a new approach to variational problems containing metric and connection.