  In the framework of Metric-Affine Gravity, the existing correspondence
between the Einstein tensor and the energy-momentum tensor of matter provided
by General Relativity is extended towards a post-Riemannian description in
terms of the torsion and nonmetricity fields, which are sourced by the spin,
dilation and shear currents of matter. In this work, we focus on the dynamical
role of the traceless part of the nonmetricity tensor and its intrinsic
connection with shears, defining a model which encloses a new black hole
solution endowed with shear charges. We show that the extension in the presence
of dynamical torsion and Weyl vector leads to the broadest family of static and
spherically symmetric black hole solutions with spin, dilation and shear
charges in Metric-Affine Gravity so far.
