MG11 
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New Vacuum Solutions for Quadratic Metric-affine Gravity

A classical pp-wave is a four-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalize this definition to metric compatible spacetimes with torsion. We use these generalized pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity and compare our model with a classical relativistic model describing the interaction of gravitational and neutrino fields, namely Einstein-Weyl theory.