AI 中文总结
该研究开发相对论框架，利用EMRI和IMRI引力波探测超大质量黑洞周围暗物质，发现暗物质晕对引力波的保守修正效应主导，未来LISA等任务可实现相关探测。
AI 中文摘要
尽管超大质量黑洞附近暗物质的分布对星系演化和引力的精确检验至关重要，但目前人们对其了解仍十分有限。未来的空间引力波天文台提供了一个独特的机会，可通过致密天体向超大质量黑洞的旋进过程来探测这一相对论性区域。基于我们此前在广义相对论框架下构建的精确爱因斯坦云解，我们开发了一套完全相对论性的框架，用于研究环绕超大质量黑洞的无碰撞暗物质晕的引力波信号。该框架对极端质量比旋进（EMRI）和中等质量比旋进（IMRI）的轨道动力学、绝热旋进、累积引力波周期、波形相位演化、信噪比及波形失配度进行了统一处理。作为代表性应用，我们将该形式体系应用于I型模型。结果表明，相对论性暗物质晕可对累积引力波周期、波形相位、信噪比及波形失配度产生可测量的修正，得出了关于可探测性的一致结论。通过将时空几何的保守修正与相对论性动力学摩擦导致的耗散效应分离，我们发现，对于所考虑的晕模型，可观测的信号特征主要由前者主导，而后者的影响可忽略不计。这些结果表明，未来LISA及类似任务的引力波观测可能为探测超大质量黑洞周围暗物质的相对论性分布和物理性质提供强大的工具。
英文摘要
The distribution of dark matter in the immediate vicinity of supermassive black holes remains poorly understood despite its importance for galaxy evolution and precision tests of gravity. Future space-based gravitational-wave observatories offer a unique opportunity to probe this relativistic regime through the inspiral of compact objects into supermassive black holes. Building upon our previously constructed exact Einstein-cloud solutions within General Relativity, we develop a fully relativistic framework to investigate the gravitational-wave signatures of collisionless dark-matter halos surrounding supermassive black holes. The framework provides a unified treatment of orbital dynamics, adiabatic inspiral, accumulated gravitational-wave cycles, waveform phase evolution, signal-to-noise ratio, and waveform mismatch for extreme- and intermediate-mass-ratio inspirals (EMRIs/IMRIs). As a representative application, we specialize the formalism to Model I. We show that relativistic dark-matter halos can produce measurable modifications to the accumulated gravitational-wave cycles, waveform phase, signal-to-noise ratio, and waveform mismatch, leading to consistent conclusions regarding detectability. By separating conservative modifications of the spacetime geometry from dissipative effects due to relativistic dynamical friction, we find that the observable signatures are dominated by the former, while the latter remains negligible for the halo models considered. These results demonstrate that future gravitational-wave observations by LISA and similar missions may provide a powerful probe of the relativistic distribution and physical nature of dark matter around supermassive black holes.
Comments18 pages, 8 figures
