  The approach of metric-affine gravity initially distinguishes it from
Einstein's general relativity. Using an independent affine connection produces
a theory with 10+64 unknowns. We write down the Yang-Mills action for the
affine connection and produce the Yang-Mills equation and the so called
complementary Yang-Mills equation by independently varying with respect to the
connection and the metric respectively. We call this theory the Yang-Mielke
theory of gravity. We construct explicit spacetimes with pp-metric and purely
axial torsion and show that they represent a solution of Yang-Mills theory.
Finally we compare these spacetimes to existing solutions of metric-affine
gravity and present future research possibilities.
