Dereli, TekinŞenikoğlu, Yorgo2024-07-122024-07-122023Dereli, T. and Şenikoğlu, Y. (2023). Weyl neutrinos in plane symmetric spacetimes. General Relativity and Gravitation, 55(11), p.1-20.10.1007/s10714-023-03175-82-s2.0-85175343829https://doi.prg/10.1007/s10714-023-03175-8https://hdl.handle.net/20.500.12415/3258We investigate complex quaternion-valued exterior differential forms over 4-dimensional Lorentzian spacetimes and explore Weyl spinor fields as minimal left ideals within the complex quaternion algebra. The variational derivation of the coupled Einstein–Weyl equations from an action is presented, and the resulting field equations for both first and second order variations are derived and simplified. Exact plane symmetric solutions of the Einstein–Weyl equations are discussed, and two families of exact solutions describing left-moving and right-moving neutrino plane waves are provided. The study highlights the significance of adjusting a quartic self-coupling of the Weyl spinor in the action to ensure the equivalence of the field equations.eninfo:eu-repo/semantics/openAccessNeutrino wavesPlane symmetric spacetimesWeyl equationExact solutionsGeneral relativityArticle2011155