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PreprintarXiv licencearXiv

Exact Solutions for Colliding Neutrino Waves and the Absence of Mutual Scattering for a Single Grassmann Mode

  • Yorgo Senikoglu
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Abstract

We study the head-on collision of two plane neutrino waves in the coupled Einstein-Weyl system, treating the massless Weyl spinor as an odd Grassmann valued field. We show that the mixed components of the Einstein equations force the two counter propagating waves to be built on a single Grassmann mode, whose bilinear ε=ηη* is nilpotent. With this structure the full coupled system is solved exactly in the interaction region for arbitrary amplitude and phase profiles, and the metric and spinor fields are matched to the single wave regions by the non-impulsive O'Brien-Synge junction conditions. The metric functions contain no terms coupling the two waves; the Weyl scalar Ψ2 vanishes, and Ψ0, Ψ4 are proportional to the neutrino energy fluxes. The waves therefore traverse each other without mutual scattering; we trace this to the nilpotency of the single mode bilinear. We discuss the limits of this result and indicate where cross couplings can arise.

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Cite

BibTeXRIS
BibTeX
@misc{senikoglu2026exact,
  title = {{Exact Solutions for Colliding Neutrino Waves and the Absence of Mutual Scattering for a Single Grassmann Mode}},
  author = {Yorgo Senikoglu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04321},
  eprint = {2610.04321},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04321},
}
RIS
TY  - UNPB
TI  - Exact Solutions for Colliding Neutrino Waves and the Absence of Mutual Scattering for a Single Grassmann Mode
AU  - Yorgo Senikoglu
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04321
UR  - https://arxiv.org/abs/2610.04321
AB  - We study the head-on collision of two plane neutrino waves in the coupled Einstein-Weyl system, treating the massless Weyl spinor as an odd Grassmann valued field. We show that the mixed components of the Einstein equations force the two counter propagating waves to be built on a single Grassmann mode, whose bilinear ε=ηη^* is nilpotent. With this structure the full coupled system is solved exactly in the interaction region for arbitrary amplitude and phase profiles, and the metric and spinor fields are matched to the single wave regions by the non-impulsive O'Brien-Synge junction conditions. The metric functions contain no terms coupling the two waves; the Weyl scalar Ψ_2 vanishes, and Ψ_0, Ψ_4 are proportional to the neutrino energy fluxes. The waves therefore traverse each other without mutual scattering; we trace this to the nilpotency of the single mode bilinear. We discuss the limits of this result and indicate where cross couplings can arise.
ER  -