Gravitational field of spinors with torsion and matter−antimatter asymmetry

@misc{poplawski2026gravitational,
  title = {{Gravitational field of spinors with torsion and matter$-$antimatter asymmetry}},
  author = {Nikodem Popławski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38738},
  eprint = {2610.38738},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38738},
}

TY  - UNPB
TI  - Gravitational field of spinors with torsion and matter−antimatter asymmetry
AU  - Nikodem Popławski
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38738
UR  - https://arxiv.org/abs/2610.38738
AB  - The conservation law for the orbital plus spin angular momentum of a free Dirac particle in curved spacetime requires that the affine connection has the antisymmetric part: the torsion tensor, which extends general relativity to the Einstein−Cartan theory of gravity. In spacetime with torsion, the Dirac equation becomes a nonlinear, cubic equation in the spinor wave function. Under charge conjugation, the nonlinear term changes sign relative to the mass term. A Dirac spinor and its charge conjugate therefore satisfy different field equations. We use the spinor connection formalism to derive the Dirac equation for a spherical spinor in its centrally symmetric gravitational field with torsion. We determine the energy−momentum tensor for this spinor and show that the energy contribution from torsion is negative for matter particles and positive for antimatter particles. Consequently, the ground state of a fermion has a lower energy than the ground state of the corresponding antifermion. We also derive the Einstein−Cartan−Dirac equations for this spinor; they indicate the existence of particle-like soliton solutions exhibiting matter−antimatter energy asymmetry.
ER  -