New vacuum solutions for quadratic metric–affine gravity

Abstract

In this thesis we deal with quadratic metric–affine gravity, which is an alternative theory of gravity. We present new vacuum solutions for this theory and attempt to give their physical interpretation on the basis of comparison with existing classical models. These new explicit vacuum solutions of quadratic metric–affine gravity are constructed using generalised pp-waves. A classical pp-wave is a 4-dimensional Lorentz–ian spacetime which admits a non–vanishing parallel spinor field. We generalise this definition to metric compatible spacetimes with torsion, describe basic properties of such spacetimes and eventually use them to construct new solutions to the field equations of quadratic metric–affine gravity. The physical interpretation of these solutions we propose in this thesis is that these new solutions represent a conformally invariant metric–affine model for a massless elementary particle. We give a comparison with a classical model describing the interaction of gravitational and massless neutrino fields, namely Einstein-Weyl theory.EThOS - Electronic Theses Online ServiceGBUnited Kingdo