2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96613A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.17 pages, LaTeX2eGeneral Relativity and Quantum CosmologyDifferential Geometrytext