Rotating Black Holes in Metric-Affine Gravity
  Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially symmetric exact solution of the vacuum field equations. This black hole solution embodies a Kerr-deSitter metric and the post-Riemannian structures of torsion and nonmetricity. The solution is characterized by mass, angular momentum, and shear charge, the latter of which is a measure for violating Lorentz invariance. 
Peter Baekler and Friedrich W. Hehl