AI 中文总结
研究史瓦西时空中自旋测试粒子运动，在特定近似和条件下，推导相关物理量，构建周期轨道，关联李雅普诺夫指数与分离线结构，提供解析联系，还研究了此类粒子周期轨道产生的引力波。
AI 中文摘要
我们在马蒂松 - 帕帕佩特鲁 - 狄克逊极 - 偶极近似下，研究史瓦西时空中自旋测试粒子的运动，并施加图尔齐耶夫 - 狄克逊自旋补充条件。限制在赤道轨道且粒子自旋与轨道角动量对齐，保留特定自旋\(s\)的线性项，我们推导出自旋修正的径向势、圆轨道条件、束缚周期轨道、周转频率以及不稳定圆轨道的李雅普诺夫指数。自旋 - 曲率耦合使圆轨道能量和角动量发生偏移，将最内稳定圆轨道移至\(r_{\rm ISCO}=6M - 2\sqrt{2/3}\,s+\mathcal{O}(s^2)\)。我们用莱文 - 佩雷斯 - 吉兹变焦 - 旋转分类法构建束缚周期轨道，展示粒子自旋如何使相应的能量 - 角动量图变形。然后获得坐标时间方位角和径向周转频率，并将其用作相对论进动和准周期振荡共振处方的运动学输入。最后，将不稳定圆轨道的李雅普诺夫指数与控制近同宿变焦 - 旋转运动的局部分离线结构相关联。所得公式在非旋转黑洞背景下，在自旋线性的MPD动力学、周期轨道分类法、周转频率偏移和瞬态强场现象学之间提供了紧凑的解析联系。此外，我们研究了围绕黑洞的大质量自旋粒子周期轨道产生的引力波，展示了与涉及恒星质量紧凑自旋物体绕超大质量黑洞的极端质量比吸积相关的引力波。
英文摘要
We study the motion of spinning test particles in Schwarzschild spacetime within the Mathisson--Papapetrou--Dixon pole--dipole approximation, imposing the Tulczyjew--Dixon spin supplementary condition. Restricting to equatorial orbits with the particle spin aligned with the orbital angular momentum, and retaining terms through linear order in the specific spin $s$, we derive the spin-corrected radial potential, circular-orbit conditions, bound periodic trajectories, epicyclic frequencies, and Lyapunov exponents of unstable circular orbits. The spin--curvature coupling shifts the circular-orbit energy and angular momentum and moves the innermost stable circular orbit to $r_{\rm ISCO}=6M-2\sqrt{2/3}\,s+\mathcal{O}(s^2)$ in the sign convention adopted here. We construct bound periodic orbits using the Levin--Perez-Giz zoom--whirl taxonomy and show how the particle spin deforms the corresponding energy--angular-momentum map. We then obtain the coordinate-time azimuthal and radial epicyclic frequencies and use them as kinematical inputs for relativistic-precession and resonance prescriptions for quasi-periodic oscillations. Finally, we relate the Lyapunov exponent of unstable circular orbits to the local separatrix structure governing near-homoclinic zoom--whirl motion. The resulting formulation provides a compact analytic connection between linear-in-spin MPD dynamics, periodic-orbit taxonomy, epicyclic-frequency shifts, and transient strong-field phenomenology in a nonrotating black-hole background. Also, we study the gravitational waveforms from the periodic orbits of a massive spinning particle around a black hole, presenting those associated with extreme mass-ratio inspirals involving a stellar-mass compact spinning object orbiting a supermassive black hole.
Comments18 pages, 11 figures
