[2101.04212] Spinors with torsion and matter$-$antimatter asymmetry Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search General Relativity and Quantum Cosmology arXiv:2101.04212 (gr-qc) [Submitted on 11 Jan 2021 ( v1 ), last revised 25 Apr 2026 (this version, v3)] Title: Spinors with torsion and matter$-$antimatter asymmetry Authors: Nikodem Popławski View a PDF of the paper titled Spinors with torsion and matter$-$antimatter asymmetry, by Nikodem Pop{\l}awski View PDF HTML (experimental) Abstract: 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 the presence of torsion, the Dirac equation becomes a nonlinear, cubic equation in the spinor wave function. We show that the energy eigenvalues of the corresponding Hamiltonian as functions of the momentum are different for the fermion and antifermion components of the spinor, violating charge conjugation symmetry, and also depend on the helicity. Consequently, particles of matter and antimatter have different dispersion relations and therefore different masses. This mass difference increases with density and becomes significant near the Cartan density, which existed in the early Universe. Because antimatter particles were more massive than matter particles, they were also slower during pair production in the early Universe and therefore had higher cross sections for gravitational capture by primordial black holes. This difference might have led to the matter$-$antimatter imbalance in the observable Universe: the missing antimatter fell into black holes. Comments: 8 pages Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Quantum Physics (quant-ph) Cite as: arXiv:2101.04212 [gr-qc] (or arXiv:2101.04212v3 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2101.04212 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nikodem Poplawski [ view email ] [v1] Mon, 11 Jan 2021 22:06:27 UTC (9 KB) [v2] Sun, 1 Feb 2026 00:42:36 UTC (8 KB) [v3] Sat, 25 Apr 2026 22:13:28 UTC (11 KB) Full-text links: Access Paper: View a PDF of the paper titled Spinors with torsion and matter$-$antimatter asymmetry, by Nikodem Pop{\l}awski View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2021-01 Change to browse by: quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from