PP-waves with torsion: a metric-affine model for the massless neutrino

  • Vedad Pasic
  • Elvis Barakovic
Research Article


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. We then 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.


Quadratic metric-affine gravity pp-Waves Torsion Massless neutrino Einstein–Weyl theory 



The authors are very grateful to D Vassiliev, J B Griffiths and F W Hehl for helpful advice and to the Ministry of Education and Science of the Federation of Bosnia and Herzegovina, which supported our research.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TuzlaTuzlaBosnia and Herzegovina

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