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Rotating Weyssenhoff fluids in linearized Einstein-Cartan theory

Emmanuele Battista1,*, Salvatore Capozziello2,3,4,†, and Francesco Giovinetti2,3,‡

  • *Contact author: ebattista@lnf.infn.it
  • †Contact author: capozziello@na.infn.it
  • ‡Contact author: francesco.giovinetti@unina.it
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Phys. Rev. D 114, 084044 – Published 15 October, 2026

DOI: https://doi.org/10.1103/7vn8-nqh4

Abstract

The Weyssenhoff fluid expands the ordinary perfect-fluid description of general relativity by taking into account the intrinsic spin of its constituent particles. Within the linearized regime of Einstein-Cartan theory, we investigate the exterior geometry produced by isolated slowly rotating Weyssenhoff fluids, i.e., sources endowed with both macroscopic and microscopic angular momenta. Our work represents an extension of the foundational analysis of Arkuszewski, Kopczyński and Ponomariev, which was restricted to the static fluid configuration. Under the assumptions of stationarity and axial symmetry, we derive the explicit expression for the linearized stress-energy tensor of the source and obtain the corresponding metric through a multipole expansion. The ensuing solution exhibits a generalized Lense-Thirring structure, with both the gravitoelectric and gravitomagnetic sectors affected by the quantum spin and macroscopic rotation. We also discuss some phenomenological implications of the model, including the gyroscope precession and the Sagnac effect, along with potential experimental probes of the predicted corrections.

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Phys. Rev. D 114, 084044– Published 15 October, 2026
  • Received 20 August 2026
  • Accepted 23 September 2026
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