An axially symmetric solution of metric-affine gravity
  We present an exact stationary {\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges. 
E.J. Vlachynsky, R. Tresguerres, Yu.N. Obukhov, and F.W. Hehl