New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

Abstract

In this paper we present an overview of our research that was presented at theMASSEE International Congress on Mathematics MICOM 2009 in Ohrid, Macedonia. We deal with quadratic metric–affine gravity, which is an alternative theory of gravity. We present new vacuum solutions for this theory and an 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 Lorentzian 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 is that these new solutions represent a conformally invariant metric–affine model for the massless neutrino. We give a comparison with a classical model describing the interaction of gravitational and massless neutrino fields, namely Einstein-Weyl theory. Future research topics are briefly discussed.