PP-waves with Torsion - a Metric-affine Model for the Massless Neutrino

TL;DR

This paper introduces a new class of solutions in quadratic metric-affine gravity called generalized pp-waves with torsion, proposing they model massless neutrinos and comparing them to Einstein-Weyl theory solutions.

Contribution

The paper develops generalized pp-wave solutions with torsion in quadratic metric-affine gravity, offering a novel geometric model for massless neutrinos.

Findings

Generalized pp-waves of parallel Ricci curvature are explicit vacuum solutions.

These solutions are conformally invariant and resemble Einstein-Weyl pp-waves.

Proposed as a metric-affine model for massless neutrinos.

Abstract

In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A 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. This definition was generalised in our previous work to metric compatible spacetimes with torsion and used to construct new explicit vacuum solutions of quadratic metric-affine gravity, namely generalised pp-waves of parallel Ricci curvature. The physical interpretation of these solutions we propose in this article is that they represent a conformally invariant metric-affine model for a massless elementary particle. We give a comparison with the classical model describing the interaction of gravitational and massless neutrino fields, namely Einstein-Weyl theory and construct pp-wave type solutions of this theory. We point out that generalised pp-waves of parallel Ricci curvature are very similar to pp-wave type solutions of the Einstein-Weyl model and therefore propose that our generalised pp-waves of parallel Ricci curvature represent a metric-affine model for the massless neutrino.