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In the framework of Metric-Affine Gravity, the existing correspondencebetween the Einstein tensor and the energy-momentum tensor of matter providedby General Relativity is extended towards a post-Riemannian description interms 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 dynamicalrole of the traceless part of the nonmetricity tensor and its intrinsicconnection with shears, defining a model which encloses a new black holesolution endowed with shear charges. We show that the extension in the presenceof dynamical torsion and Weyl vector leads to the broadest family of static andspherically symmetric black hole solutions with spin, dilation and shearcharges in Metric-Affine Gravity so far.

New black hole solutions with a dynamical traceless nonmetricity tensor in Metric-Affine Gravity