Spin-curvature effects in slowly rotating black hole spacetime
Abstract
We investigate the spin-curvature interaction for a massive spin-1/2 quantum particle in a slowly rotating black hole spacetime. In contrast to the flat Minkowski space, the curved spacetime introduces non-trivial spin connections into the Dirac equation due to the direct curvature-spin interaction. The force arising from this non-trivial spin-curvature coupling makes the particle deviate from its geodesics. We first calculate the tetrads in the co-moving frame of the particle in the slowly rotating black hole background. We then compute the components of the relativistic quantum force, arising from the spin-curvature interaction, using these co-moving tetrads up to linear order in the rotation parameter (a) of the black hole. The procedure of computing the force is based on the WKB approximation and the Gordon decomposition method for the Dirac probability four current. Our results show that the rotation parameter modifies the magnitude of the force by introducing a term that decays more rapidly with radial distance than the force magnitude in a static spherically symmetric Schwarzschild black hole spacetime.
Related
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BibTeX
@misc{jana2026spincurvature,
title = {{Spin-curvature effects in slowly rotating black hole spacetime}},
author = {Arpita Jana and Subhajit Mazumdar and Sunandan Gangopadhyay},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24364},
eprint = {2609.24364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24364},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-curvature effects in slowly rotating black hole spacetime
AU - Arpita Jana
AU - Subhajit Mazumdar
AU - Sunandan Gangopadhyay
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24364
UR - https://arxiv.org/abs/2609.24364
AB - We investigate the spin-curvature interaction for a massive spin-1/2 quantum particle in a slowly rotating black hole spacetime. In contrast to the flat Minkowski space, the curved spacetime introduces non-trivial spin connections into the Dirac equation due to the direct curvature-spin interaction. The force arising from this non-trivial spin-curvature coupling makes the particle deviate from its geodesics. We first calculate the tetrads in the co-moving frame of the particle in the slowly rotating black hole background. We then compute the components of the relativistic quantum force, arising from the spin-curvature interaction, using these co-moving tetrads up to linear order in the rotation parameter (a) of the black hole. The procedure of computing the force is based on the WKB approximation and the Gordon decomposition method for the Dirac probability four current. Our results show that the rotation parameter modifies the magnitude of the force by introducing a term that decays more rapidly with radial distance than the force magnitude in a static spherically symmetric Schwarzschild black hole spacetime.
ER -