The Biconnection Variational Principle for General Relativity

TL;DR

This paper revisits a variational approach to general relativity involving two independent affine connections, showing it reduces to Einstein's equations regardless of matter action dependence.

Contribution

It clarifies and revises the biconnection variational principle, demonstrating its consistency with Einstein's equations for any matter connection dependence.

Findings

Field equations reduce to Einstein's equations

Approach is valid for any matter connection dependence

Provides a revised understanding of the biconnection variational principle

Abstract

A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein field equations for any dependence of the matter action upon an independent connection.