A covariant approach to the Dirac field in LRS space-times

Article

A covariant approach to the Dirac field in LRS space-times

Vignolo S.; De Maria G.; Fabbri L.; Carloni S.

Class. Quantum Grav. 42(21), 215013 (2025)

Abstract

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.

Institute authors

Carloni, Sante

BibTeX

@article{UTF1027,
  author        = {Vignolo S. and De Maria G. and Fabbri L. and Carloni S.},
  title         = {{A covariant approach to the Dirac field in LRS space-times}},
  journal       = {Class. Quantum Grav.},
  volume        = {42},
  number        = {21},
  pages         = {215013},
  year          = {2025},
  doi           = {10.1088/1361-6382/ae134b},
  eprint        = {2507.03432},
  archivePrefix = {arXiv},
  url           = {https://doi.org/10.1088/1361-6382/ae134b},
}