Matter Lagrangians Coupled with Connections

TL;DR

This paper explores extended gravitational theories in the metric-affine formalism where matter interacts directly with the connection, providing a general method to solve the associated field equations and analyzing special cases.

Contribution

It introduces a comprehensive procedure for solving connection field equations in metric-affine gravity with matter coupling, extending previous analyses.

Findings

General solution method for connection equations

Analysis of no-coupling and specific cases

Framework applicable to various extended gravitation theories

Abstract

We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to the connection. As special cases one has the no-coupling case (which is standard in f(R) literature) as well as the cases already analyzed in ref.[1].