The Dirac field in LRS space-times: a covariant approach
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914554080919552 |
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| author | Vignolo, Stefano De Maria, Giuseppe Carloni, Sante Fabbri, Luca |
| author_facet | Vignolo, Stefano De Maria, Giuseppe Carloni, Sante Fabbri, Luca |
| contents | We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices. Within this framework, we analyze the conditions under which a self-gravitating Dirac field can be consistently embedded in Locally Rotationally Symmetric (LRS) space-times of types I, II, and III. In accordance with the LRS symmetry requirements, we extend a previous work by assuming that the velocity and spin vector fields of the Dirac field lie in the planes defined pointwise by the generators of the time-like and space-like congruences, which underlie the $(1+1+2)$ decomposition. We present some analytical and numerical solutions to illustrate the applicability of the proposed framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10620 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Dirac field in LRS space-times: a covariant approach Vignolo, Stefano De Maria, Giuseppe Carloni, Sante Fabbri, Luca General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 83C99 We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices. Within this framework, we analyze the conditions under which a self-gravitating Dirac field can be consistently embedded in Locally Rotationally Symmetric (LRS) space-times of types I, II, and III. In accordance with the LRS symmetry requirements, we extend a previous work by assuming that the velocity and spin vector fields of the Dirac field lie in the planes defined pointwise by the generators of the time-like and space-like congruences, which underlie the $(1+1+2)$ decomposition. We present some analytical and numerical solutions to illustrate the applicability of the proposed framework. |
| title | The Dirac field in LRS space-times: a covariant approach |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 83C99 |
| url | https://arxiv.org/abs/2605.10620 |