Analytic motions of spinning particles in Schwarzschild-(anti-)de Sitter spacetime
Abstract
The motion of a spinning test particle in a static, spherically symmetric spacetime with a cosmological constant is studied within the Mathisson-Papapetrou-Dixon formalism, working to linear order in the particle's spin. By exploiting the symmetries of the background, the radial and latitudinal dynamics are reduced to first-order equations governed by a spin-deformed quintic polynomial. A complete classification of the real root structure of this quintic is carried out, from which the allowed orbital types for spinning particles in the Schwarzschild-anti-de Sitter and Schwarzschild-de Sitter geometries follow directly. The parameter dependence of the root structure and of the stable circular orbit interval is analyzed. In particular, for values of the cosmological constant beyond the Stuchlík limit, where spinless particles admit no bound orbits, spinning particles can still remain bound. The radial motion is expressed piecewise in terms of Lauricella hypergeometric functions, with the simple positive real roots of the quintic acting as branch cuts. The latitudinal motion consists of small oscillations about an equatorial plane, and its phase, governed by the same quintic, admits an analogous analytic representation.
Related
- Dynamics of spinning test particles in the innermost stable circular orbit of an approximate Kerr-like spacetime with mass quadrupole
- Analytic Electromagnetic Effective Source for Geodesic Orbit in Schwarzschild Spacetime
- Exact dynamics and the spin wall for large-spin particles in Schwarzschild spacetime
- Multi-Boundary Spinning AdS5 Black Holes, Strongly Coupled Plasma Balls and a dual locally de Sitter spacetime
- Mapping Schwarzschild Spacetime: From Kruskal to Diamond and Golden Representations
BibTeX
@misc{li2026analytic,
title = {{Analytic motions of spinning particles in Schwarzschild-(anti-)de Sitter spacetime}},
author = {Rui-Hui Li and Xing-You Zhou and Chao-Jun Feng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09755},
eprint = {2609.09755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09755},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytic motions of spinning particles in Schwarzschild-(anti-)de Sitter spacetime
AU - Rui-Hui Li
AU - Xing-You Zhou
AU - Chao-Jun Feng
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09755
UR - https://arxiv.org/abs/2609.09755
AB - The motion of a spinning test particle in a static, spherically symmetric spacetime with a cosmological constant is studied within the Mathisson-Papapetrou-Dixon formalism, working to linear order in the particle's spin. By exploiting the symmetries of the background, the radial and latitudinal dynamics are reduced to first-order equations governed by a spin-deformed quintic polynomial. A complete classification of the real root structure of this quintic is carried out, from which the allowed orbital types for spinning particles in the Schwarzschild-anti-de Sitter and Schwarzschild-de Sitter geometries follow directly. The parameter dependence of the root structure and of the stable circular orbit interval is analyzed. In particular, for values of the cosmological constant beyond the Stuchlík limit, where spinless particles admit no bound orbits, spinning particles can still remain bound. The radial motion is expressed piecewise in terms of Lauricella hypergeometric functions, with the simple positive real roots of the quintic acting as branch cuts. The latitudinal motion consists of small oscillations about an equatorial plane, and its phase, governed by the same quintic, admits an analogous analytic representation.
ER -