A covariant approach to the Dirac field in LRS space-times
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914072293801984 |
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| author | Vignolo, Stefano De Maria, Giuseppe Fabbri, Luca Carloni, Sante |
| author_facet | Vignolo, Stefano De Maria, Giuseppe Fabbri, Luca Carloni, Sante |
| contents | We use the polar decomposition to describe the Dirac field in terms of an effective spinorial fluid. After reformulating all covariant equations in ``spinorial'' signature $(+ -- )$, we develop a $(1+1+2)$ covariant approach for the Dirac field that does not require the use of tetrad fields or Clifford matrices. By identifying the velocity and spin fields as the generators of time-like and space-like congruences, we examine the compatibility of a self-gravitating Dirac field with Locally Rotationally Symmetric space-times of types I, II, and III. We provide illustrative examples to demonstrate the effectiveness of our construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A covariant approach to the Dirac field in LRS space-times Vignolo, Stefano De Maria, Giuseppe Fabbri, Luca Carloni, Sante General Relativity and Quantum Cosmology Mathematical Physics We use the polar decomposition to describe the Dirac field in terms of an effective spinorial fluid. After reformulating all covariant equations in ``spinorial'' signature $(+ -- )$, we develop a $(1+1+2)$ covariant approach for the Dirac field that does not require the use of tetrad fields or Clifford matrices. By identifying the velocity and spin fields as the generators of time-like and space-like congruences, we examine the compatibility of a self-gravitating Dirac field with Locally Rotationally Symmetric space-times of types I, II, and III. We provide illustrative examples to demonstrate the effectiveness of our construction. |
| title | A covariant approach to the Dirac field in LRS space-times |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2507.03432 |