An exact solution of the metric-affine gauge theory with dilation,   shear, and spin charges
  The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses {\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation, shear and spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation, shear and spin charges. 
Yu.N. Obukhov, E.J. Vlachynsky, W. Esser, R. Tresguerres, and F.W.   Hehl