AI 中文总结
该研究探究共形反常修正极端质量比旋近引力波中的混沌印记，采用数值拼凑法分析发现混沌轨道的引力波信号与规则轨道差异显著，未来空间引力波探测器可探测该信号，为探测共形反常修正提供潜在途径。
AI 中文摘要
本研究探究中心黑洞经量子共形反常修正后的极端质量比旋近（EMRI）引力波信号中混沌轨道的影响。我们采用数值拼凑法（numerical kludge method）计算致密天体沿不同轨道产生的引力波形，推导对应的引力波频率分布与能谱。计算表明，轨道能量或反常系数的变化会驱动轨道演化从规则可积运动转向混沌运动，这种动力学转变会在引力波信号中留下清晰印记。具体而言，来自混沌轨道的引力波具有显著的不规则且随时间变化的振幅波动，在频率域和能量域均伴随丰富的精细谱峰与扩展的连续谱分布，这与规则非混沌轨道产生的引力辐射截然不同。此外，我们通过将不同轨道上致密天体发射的引力波特征应变与未来空间引力波探测器（包括LISA、太极（Taiji）、天琴（TianQin））的灵敏度曲线对比，评估其可探测性。结果显示，这些探测器能够捕获经共形反常修正的混沌系统的引力波信号，为天文观测中探测共形反常修正提供了潜在途径。
英文摘要
In this work, we investigate the effect of chaotic orbits on the extreme mass ratio inspiral (EMRI) gravitational wave signals where the central black hole is corrected by quantum conformal anomaly. We utilize the numerical kludge method to compute gravitational waveforms produced by the compact object along different orbital trajectories, and also derive the corresponding frequency distribution and energy spectra of gravitational waves. Our calculations reveal that variations in orbital energy or anomaly coefficient drive the orbital evolution from regular integrable motion to chaotic motion, and such dynamical transition leaves clear imprints on gravitational-wave signal. Specifically, gravitational waves originating from chaotic orbits feature pronounced irregular and time-varying amplitude fluctuations, accompanied by abundant fine spectral spikes and extended continuous spectral distributions in both frequency and energy domains, which differ drastically from the gravitational radiation generated by the regular non-chaotic orbits. Moreover, we evaluate the detectability by comparing the calculated characteristic strain of gravitational waves emitted by the compact object on different orbits with the sensitivity curves of future space-based GW detectors, including LISA, Taiji and TianQin. The results demonstrate that these detectors are capable of capturing gravitational-wave signals from chaotic systems modified by conformal anomalies, which provide a potential pathway for detecting conformal anomaly correction in astronomical observation.
Commentsv1: 16 pages, 10 figures
