Stability in cubic metric-affine gravity

We analyze the stability issue of the vector and axial modes of the torsion and nonmetricity tensors around general backgrounds in the framework of cubic metric-affine gravity. We show that the presence of cubic order invariants defined from the curvature, torsion, and nonmetricity tensors allow the cancellation of the well-known instabilities arising in the vector and axial sectors of quadratic metric-affine gravity. For the resulting theory, we also obtain Reissner-Nordstr"om-like black hole solutions with dynamical torsion and nonmetricity, which in general include massive tensor modes for these quantities, thus avoiding further no-go theorems that potentially prevent a consistent interaction of massless higher spin fields in the quantum regime.