Dark matter (DM) constitutes the predominant portion of matter in our Universe. Despite compelling evidence, the precise characteristics of DM remain elusive. Among the leading DM candidates are weakly interacting massive particles, which may clump into steep concentrations around the central black holes of galaxies. However, DM profiles of the resulting dense spikes remain uncertain. Here we employ the relativistic dynamics in Schwarzschild geometry and first evaluate the velocity distributions of DM within such spikes. Through variations in black hole masses and dark halo parameters, we identify universal features in DM profiles and fit them with Gaussian distributions. Additionally, we illustrate the impact of dynamical friction on gravitational waves generated by extreme-mass-ratio inspirals within DM spikes, taking into account the velocity distribution of DM in the relativistic regime. Our findings demonstrate the phase shifts in the time-domain waveform, potentially providing useful insights for probing DM in galactic centers by gravitational-wave experiments.

中文翻译：

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黑洞周围尖峰中暗物质的速度分布以及极端质量比引流对引力波的影响


暗物质 （DM） 构成了我们宇宙中物质的主要部分。尽管证据令人信服，但 DM 的确切特征仍然难以捉摸。主要的 DM 候选者是弱相互作用的大质量粒子，它们可能会在星系的中心黑洞周围聚集成陡峭的浓度。然而，由此产生的密集尖峰的 DM 剖面仍然不确定。在这里，我们采用 Schwarzschild 几何中的相对论动力学，并首先评估 DM 在这种尖峰内的速度分布。通过黑洞质量和暗晕参数的变化，我们确定了 DM 剖面中的普遍特征，并用高斯分布对其进行拟合。此外，考虑到相对论状态下 DM 的速度分布，我们说明了动力摩擦对 DM 尖峰内极端质量比螺旋产生的引力波的影响。我们的研究结果证明了时域波形中的相移，可能为通过引力波实验探测星系中心的 DM 提供有用的见解。