Variational techniques in general relativity: a metric-affine approach to Kaluza's theory

A new variational principle for General Relativity, based on an action functional involving both the metric tensor and the affine connection as independent degrees of freedom is presented. The resulting extremals are seen to be pairs consisting of a Ricci flat metric and of the associated Riemannian connection. An application to Kaluza's theory of interacting gravitational and electromagnetic fields is discussed.