Variational techniques in general relativity: A metric-affine approach to Kaluzas theory

A new variational principle for General Relativity, based on an action functional $I/(Phi, abla)/$ involving both the metric $Phi/$ and the connection $ abla/$ as independent, emph{unconstrained/} degrees of freedom is presented. The extremals of $I/$ are seen to be pairs $/(Phi, abla)/$ in which $Phi/$ is a Ricci flat metric, and $ abla/$ is the associated Riemannian connection. An application to Kaluzas theory of interacting gravitational and electromagnetic fields is discussed.