Rotating Weyssenhoff fluids in linearized Einstein-Cartan theory
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, Kopczy{ń}ski 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.
Versions
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BibTeX
@misc{battista2026rotating,
title = {{Rotating Weyssenhoff fluids in linearized Einstein-Cartan theory}},
author = {Emmanuele Battista and Salvatore Capozziello and Francesco Giovinetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30545},
eprint = {2609.30545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30545},
}
RIS
TY - UNPB
TI - Rotating Weyssenhoff fluids in linearized Einstein-Cartan theory
AU - Emmanuele Battista
AU - Salvatore Capozziello
AU - Francesco Giovinetti
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30545
UR - https://arxiv.org/abs/2609.30545
AB - 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, Kopczy{ń}ski 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.
ER -