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arXiv · 2605.10620

A covariant approach to the Dirac field in LRS space-times: the case of coplanar frames

Stefano Vignolo·Giuseppe De Maria·Sante Carloni·Luca Fabbri
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Abstract

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.

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Stefano Vignolo, Giuseppe De Maria, Sante Carloni, Luca Fabbri. 2026-05-11. A covariant approach to the Dirac field in LRS space-times: the case of coplanar frames. https://arxiv.org/abs/2605.10620

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