  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.
