发表机构
Shanghai Normal University（上海师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对史瓦西时空中大自旋粒子的平面运动，给出MPD方程的精确非微扰解，发现纯自旋起源的自旋墙，其过滤规则为非微扰现象，在致密天体吸积流中或有观测意义。
AI 中文摘要
弯曲时空中自旋测试粒子的运动由马蒂松-帕帕佩特罗-迪克森（Mathisson--Papapetrou--Dixon, MPD）方程描述，且其运动与测地线运动的偏差在自旋的一阶时就已显现。现有研究几乎都将动力学截断为自旋的线性阶，而本文在图尔齐耶夫-迪克森（Tulczyjew--Dixon）自旋补充条件下，对史瓦西时空中的平面运动给出了精确的非微扰处理：消去四速度后，MPD方程组可转化为闭合代数形式，径向运动则简化为有效势问题，全程未对自旋做任何展开。这一精确框架揭示了线性化描述中不存在、也无法获得的定性特征：最显著的是，当自旋足够大时，有效势会在仅由粒子质量和自旋决定的特征半径处出现二重根，标志着一个纯自旋起源的不可穿透的“自旋墙”；在临界自旋之上，该墙位于事件视界之外，会将视界与一般下落粒子屏蔽开。此外，自旋墙是粒子的过滤器：只有自旋、角动量与能量取特定组合的轨道才能穿透它，其余轨道都会在到达视界前被反射。线性处理中仅随自旋连续偏移的最内稳定圆轨道，在弱场极限下以闭合形式得到，且被证明在自旋足够大时不再存在。本文还计算了弱场极限下近日点进动的自旋修正，并验证了自旋为零时所有结果都退化为标准结果。自旋墙及其过滤规则是真正的非微扰现象，对自旋的任意有限阶展开都无法观测到，在致密天体周围的吸积流中具有潜在的观测信号。
英文摘要
The motion of a spinning test particle in a curved spacetime is governed by the Mathisson--Papapetrou--Dixon (MPD) equations and deviates from geodesic motion already at first order in the spin. While essentially all existing studies truncate the dynamics at linear order in the spin, we present an exact, nonperturbative treatment of planar motion in Schwarzschild spacetime under the Tulczyjew--Dixon spin supplementary condition: eliminating the four-velocity recasts the MPD system into a closed algebraic form and reduces the radial motion to an effective-potential problem, with no expansion in the spin at any stage. This exact framework uncovers qualitative features that are absent from---and in fact unattainable within---the linearized description. Most notably, for sufficiently large spin the effective potential develops a double root at a characteristic radius determined solely by the particle mass and spin, marking an impenetrable \emph{spin wall} of purely spin origin; beyond a critical spin the wall lies outside the event horizon and shields it from generic infalling particles. Moreover, the wall is a filter for particle: only orbits with a specific combinations of spin, angular momentum and energy can penetrate it, all others being reflected before reaching the horizon. In addition, the innermost stable circular orbit, which in linear treatments merely shifts continuously with spin, is obtained in closed form in the weak-field limit and is shown to cease to exist at sufficiently large spin. We further compute the spin correction to the perihelion precession in the weak-field limit and verify that all results reduce to the standard ones at vanishing spin. The spin wall and its filtering rule are genuine nonperturbative phenomena, invisible to any finite-order expansion in the spin, with potential observational signatures in accretion flows around compact objects.
