Shranjeno v:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Izdano: |
2026
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/2605.10620 |
| Oznake: |
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Kazalo:
- 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.