2014/06/30 by Vedad Pasic, Elvis Barakovic · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Curvature #Gravitation #Hypersurface #Massless particle #Neutrino #Noncommutative and Quantum Gravity Theories #Spacetime #Spinor #Tetrad #gr-qc #math.DG
paper · pdf · doi:10.1007/s10714-014-1787-y
published as General Relativ Gravit (2014) 46:1787 · 24 pages. Corrected two references. The final publication is available at springerlink.com. arXiv admin note: text overlap with arXiv:gr-qc/0505157; and text overlap with arXiv:gr-qc/0304028, arXiv:gr-qc/9402012 by other authors
openalex publication_date 2014/09/02 · arxiv created 2014/09/03 · arxiv updated 2014/09/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.