Bulgarian Academy of Sciences - National Committee for Mathematics
Citation:
Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 329p-340p
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.