Routh Reduction of Palatini Gravity in Vacuum

Abstract

An interpretation of Einstein-Hilbert gravity equations as a Lagrangian reduction of Palatini gravity is made. The main technique involved in this task consists of representing the equations of motion as a set of differential forms on a suitable bundle. In this setting, Einstein-Hilbert gravity can be considered as a kind of Routh reduction of the underlying field theory for Palatini gravity. As a byproduct of this approach, a novel set of conditions for the existence of a vielbein for a given metric is found.