Routh Reduction of Palatini Gravity in Vacuum

TL;DR

This paper interprets Einstein-Hilbert gravity as a Routh reduction of Palatini gravity using differential forms, providing new conditions for the existence of a vielbein for a given metric.

Contribution

It introduces a novel interpretation of Einstein-Hilbert gravity as Routh reduction of Palatini gravity and derives new conditions for vielbein existence.

Findings

Einstein-Hilbert gravity can be viewed as Routh reduction of Palatini gravity.

New conditions for the existence of a vielbein are established.

The approach uses differential forms on a suitable bundle.

Abstract

An interpretation of Einstein-Hilbert gravity equations as Lagrangian reduction of Palatini gravity is made. The main technique involved in this task consists in 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.