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Covariant approach to the Dirac field in locally rotationally symmetric space-times: The case of coplanar frames

Stefano Vignolo1,3,*, Giuseppe De Maria1,2,†, Sante Carloni1,2,3,‡, and Luca Fabbri1,2,3,§

  • *Contact author: stefano.vignolo@unige.it
  • †Contact author: giuseppe.demaria@edu.unige.it
  • ‡Contact author: sante.carloni@unige.it
  • §Contact author: luca.fabbri@unige.it
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APS Open Sci. 1, 000142 – Published 18 September, 2026

DOI: https://doi.org/10.1103/qfy6-mrh7

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 timelike and spacelike 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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APS Open Sci. 1, 000142– Published 18 September, 2026
Vol. 1
  • Received 12 May 2026
  • Accepted 27 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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