A New Representation of the Field Equations of Quadratic Metric-Affine Gravity

TL;DR

This paper introduces a new explicit representation of the field equations in quadratic metric-affine gravity, broadening the understanding of possible solutions without assuming specific torsion properties.

Contribution

It provides a novel explicit form of the field equations in QMAG and discusses potential new solutions, including conjectures on their existence.

Findings

Presented a new explicit representation of QMAG field equations

Reviewed existing research and solution approaches in QMAG

Proposed conjectures for new solution types in QMAG

Abstract

We deal with quadratic metric-affine gravity (QMAG), which is an alternative theory of gravity and present a new explicit representation of the field equations of this theory. In our previous work we found new explicit vacuum solutions of QMAG, namely generalised pp-waves of parallel Ricci curvature with purely tensor torsion. Here we do not make any assumptions on the properties of torsion and write down our field equations accordingly. We present a review of research done thus far by several authors in finding new solutions of QMAG and different approaches in generalising pp-waves. We present two conjectures on the new types of solutions of QMAG which the ansatz presented in this paper will hopefully enable us to prove.