发表机构
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL; Theoretical Astrophysics, Institute for Astronomy and Astrophysics, University of Tübingen; School of Applied Mathematical and Physical Sciences – SEMFE, Physics Department, National Technical University of Athens; Dipartimento di Fisica, Sapienza Università di Roma; INFN, Sezione di Roma; Birla Institute of Technology and Science Pilani（里斯本大学高等理工学院; 蒂宾根大学天文与天体物理研究所; 雅典国立技术大学应用数理科学与物理学院; 罗马智慧大学物理系; 意大利国家核物理研究院罗马分部; 比拉理工科学皮拉尼分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨潮汐增强共振对极端质量比旋近（EMRI）混沌的影响，识别混沌转变的平台，分析混沌对轨道取向的敏感性，为EMRI潮汐共振提供新的相空间表征。
AI 中文摘要
极端质量比旋近（EMRI）为探测强场引力与复杂相对论动力学提供了独特实验室。本研究探讨了一个受潮汐形变的EMRI，由恒星级次级天体绕超大质量（非）旋转黑洞运动，且该系统嵌入外部绝热变化的潮汐环境中。这类系统是相对论三体问题的受限、却符合天体物理实际的实现形式，预计出现于活动星系核中，具有明确的质量层级与辐射反应时标。外部潮汐形变打破了Kerr时空的轴对称性，使得测地线动力学不可积，进而引发混沌运动。我们通过庞加莱映射与旋转曲线（由束缚径向、极向、方位向运动的基频比值构建）表征了这种不可积性的特征。我们识别出两个显著的平台，其宽度随潮汐场振幅增大而增加，标志着从弱混沌到强混沌的转变。随后，我们证明了混沌动力学对轨道相对于潮汐场取向的敏感性。我们进一步分析了作用-角变量的固有时演化，表明与主导共振相关的角组合是相位锁定的，由此使得相关潮汐贡献能诱导运动常数的长期变化；而平台外的角组合则做循环运动。这些结果阐明了显著平台的动力学意义，并为EMRI中的潮汐共振提供了一种新颖的相空间表征。最后，我们讨论了辐射反应效应在驱动EMRI穿越潮汐岛过程中的潜在作用，以及对未来探测器引力波推断的意义。
英文摘要
Extreme-mass-ratio inspirals (EMRIs) provide a unique laboratory for probing strong-field gravity and complex relativistic dynamics. We study a tidally deformed EMRI composed of a stellar-mass secondary orbiting a supermassive (non-)rotating black hole embedded in an external, adiabatically varying tidal environment. These systems provide a restricted, yet astrophysically motivated, realization of the relativistic three-body problem, expected to appear in active galactic nuclei, with a clear hierarchy of masses and radiation-reaction timescales. The external tidal deformation breaks the axisymmetry of the Kerr spacetime, rendering the geodesic dynamics non-integrable and giving rise to chaotic motion. The resulting signature of non-integrability is characterized through Poincaré maps and rotation curves constructed from the ratios of the fundamental frequencies of bound radial, polar, and azimuthal motion. We identify two prominent plateaus whose widths increase with the tidal field amplitude, signaling a transition from weak to strong chaos. We then demonstrate the sensitivity of the chaotic dynamics to the orientation of the orbit relative to the tidal field. We further analyze the proper-time evolution of the action-angle variables, showing that the angle combinations associated with the dominant commensurabilities are phase locked, thereby allowing the associated tidal contributions to induce secular changes in the constants of motion, whereas off-plateau angle combinations circulate. These results clarify the dynamical significance of the prominent plateaus and provide a novel phase-space characterization of tidal resonances in EMRIs. Finally, we discuss the potential role of radiation-reaction effects in driving EMRIs through tidal island crossings and the implications for gravitational-wave inference with future detectors.
Comments22 pages, 11 figures
