AI 中文总结
该研究构建经典斯特默问题的相对论扩展，解析研究史瓦西时空中偶极磁层内带电粒子的圆轨道稳定性等，为致密天体磁层相关研究提供解析基础。
AI 中文摘要
我们研究嵌入外部支撑偶极磁场的史瓦西时空中相对论带电粒子的保守动力学。引力部分在各向同性坐标中被精确处理，而电磁场由相对论性外偶极解的主导渐近项描述。该公式提供了经典斯特默问题的可解析处理的相对论扩展，允许明确研究圆轨道及其稳定性结构。对于向外洛伦兹分支（以正方位运动的正符号磁耦合为特征），我们发现径向与垂直稳定性之间存在非平凡竞争：弱磁耦合将径向边际轨道向内移动，而在更强耦合下，垂直不稳定性成为限制机制，稳定圆周运动的内边界向外移动；相关垂直本轮模式逐渐软化并在垂直稳定性边界处消失。边际束缚序列呈现出独特的强耦合行为，表明能量边界与稳定性边界无需共同演化。径向和垂直本轮频率还会产生特征性可公度性，可能为非线性轨道耦合提供天然位点。由于磁场被处理为测试场，这些带电粒子效应不会改变真空史瓦西零测地线结构，因此致密天体观测中的磁信号必须源于带电物质的动力学与辐射、等离子体传播效应或超出测试场近似的物理。本文开发的框架为研究非线性动力学、辐射反作用及更真实的致密天体磁层提供了解析基础。
英文摘要
We investigate the conservative dynamics of relativistic charged particles in a Schwarzschild spacetime threaded by an externally supported dipolar magnetic field. The gravitational sector is treated exactly in isotropic coordinates, while the electromagnetic field is described by the leading asymptotic term of the relativistic exterior dipole solution. This formulation provides an analytically tractable relativistic extension of the classical Størmer problem and allows the circular-orbit and stability structure to be studied explicitly. For the outward-Lorentz branch, characterized by a positive signed magnetic coupling for positive azimuthal motion, we find a non-trivial competition between radial and vertical stability. Weak magnetic coupling shifts the radially marginal orbit inward, whereas at stronger coupling vertical instability becomes the limiting mechanism and the inner boundary of stable circular motion moves outward. The associated vertical epicyclic mode progressively softens and vanishes at the vertical stability boundary. The marginally bound sequence exhibits a distinct strong-coupling behaviour, illustrating that energetic and stability boundaries need not evolve together. The radial and vertical epicyclic frequencies also generate characteristic commensurabilities that may provide natural sites for nonlinear orbital coupling. Because the magnetic field is treated as a test field, these charged-particle effects leave the vacuum Schwarzschild null-geodesic structure unchanged. Magnetic signatures in compact-object observations must therefore arise through the dynamics and radiation of charged matter, plasma propagation effects, or physics beyond the test-field approximation. The framework developed here provides an analytical basis for studying nonlinear dynamics, radiation reaction, and more realistic compact-object magnetospheres.
Comments29 pages, 2 figures
