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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.01447 |
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| _version_ | 1866908804195549184 |
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| author | Song, Yong Fu, Jiaqi Cen, Yiting |
| author_facet | Song, Yong Fu, Jiaqi Cen, Yiting |
| contents | The spin-curvature coupling in the Mathisson-Papapetrou-Dixon (MPD) formalism induces non-geodesic motion, shifting the orbital parameters of spinning test particles in black hole spacetimes. We investigate whether these quantitative shifts alter the qualitative, global structure of the orbit manifold. Using a topological approach, we study timelike circular orbits (TCOs) for spinning particles in static, spherically symmetric spacetimes. By constructing an auxiliary vector field, we compute the topological winding number $W$ in horizon-bounded regions of asymptotically flat, anti-de Sitter (AdS), and de Sitter (dS) backgrounds. We find that $W$ is robust against both the magnitude and direction of the particle's spin: between two horizons, $W = -1$, guaranteeing at least one unstable TCO; outside the outermost horizon in asymptotically flat and AdS spacetimes, $W = 0$, enforcing that TCOs must appear in stable-unstable pairs or be absent. This spin independence reveals that the fundamental orbital structure is a property of spacetime geometry itself, not of the particle's spin. We validate this with quantitative examples in Schwarzschild, Schwarzschild-AdS, and Schwarzschild-dS spacetimes, showing explicit spin-induced TCO shifts while confirming the invariant topology. This result provides a topological foundation for interpreting gravitational waveforms from extreme mass-ratio inspirals involving spinning secondaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes Song, Yong Fu, Jiaqi Cen, Yiting General Relativity and Quantum Cosmology The spin-curvature coupling in the Mathisson-Papapetrou-Dixon (MPD) formalism induces non-geodesic motion, shifting the orbital parameters of spinning test particles in black hole spacetimes. We investigate whether these quantitative shifts alter the qualitative, global structure of the orbit manifold. Using a topological approach, we study timelike circular orbits (TCOs) for spinning particles in static, spherically symmetric spacetimes. By constructing an auxiliary vector field, we compute the topological winding number $W$ in horizon-bounded regions of asymptotically flat, anti-de Sitter (AdS), and de Sitter (dS) backgrounds. We find that $W$ is robust against both the magnitude and direction of the particle's spin: between two horizons, $W = -1$, guaranteeing at least one unstable TCO; outside the outermost horizon in asymptotically flat and AdS spacetimes, $W = 0$, enforcing that TCOs must appear in stable-unstable pairs or be absent. This spin independence reveals that the fundamental orbital structure is a property of spacetime geometry itself, not of the particle's spin. We validate this with quantitative examples in Schwarzschild, Schwarzschild-AdS, and Schwarzschild-dS spacetimes, showing explicit spin-induced TCO shifts while confirming the invariant topology. This result provides a topological foundation for interpreting gravitational waveforms from extreme mass-ratio inspirals involving spinning secondaries. |
| title | Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.01447 |