标题： 星团和暗物质作为大质量黑洞时空几何的探针 显示英文标题

标题： Star Clusters and Dark Matter as Probes of the Spacetime Geometry of Massive Black Holes

摘要： 本论文包括两个主要项目。 在第一部分中，我们评估了一种最近提出的强场广义相对论测试的可行性，其中未来对围绕银河系中心超大质量黑洞Sgr A*运行的假想恒星类别的观测，可以通过测量其轨道平面的进动来测试广义相对论所谓的无毛定理。 通过考虑中心簇中恒星和恒星级黑洞的分布如何扰动这些假想恒星的轨道，我们表明，在距离黑洞约0.2毫秒差距（约6光小时）以内的恒星，相对论进动占主导地位，从而为无毛定理的测试提供了潜在窗口。 我们的结果与N体模拟结果一致。 在第二部分中，我们开发了一个完全广义相对论的相空间表述，以考虑银河系中心超大质量黑洞Sgr A*对暗物质密度分布的影响及其在间接探测暗物质中的应用。 我们发现与Gondolo和Silk（1999）的非相对论结果存在显著差异，包括尖峰密度更高以及中心集中程度更大。 在存在大质量黑洞的情况下获得暗物质密度分布后，我们计算了其对银河系中心恒星轨道运动的扰动效应，并发现对于感兴趣的恒星，与黑洞“毛发”相关的相对论效应将主导暗物质的影响。 显示英文摘要

摘要： This thesis includes two main projects. In the first part, we assess the feasibility of a recently suggested strong-field general relativity test, in which future observations of a hypothetical class of stars orbiting very close to the supermassive black hole at the center of our galaxy, known as Sgr A*, could provide tests of the so-called no-hair theorem of general relativity through the measurement of precessions of their orbital planes. By considering how a distribution of stars and stellar mass black holes in the central cluster would perturb the orbits of those hypothetical stars, we show that for stars within about 0.2 milliparsecs (about 6 light-hours) of the black hole, the relativistic precessions dominate, leaving a potential window for tests of no-hair theorems. Our results are in agreement with N-body simulation results. In the second part, we develop a fully general relativistic phase-space formulation to consider the effects of the Galactic center supermassive black hole Sgr A* on the dark-matter density profile and its applications in the indirect detection of dark matter. We find significant differences from the non-relativistic result of Gondolo and Silk (1999), including a higher density for the spike and a larger degree of central concentration. Having the dark matter profile density in the presence of the massive black hole, we calculate its perturbing effect on the orbital motions of stars in the Galactic center, and find that for the stars of interest, relativistic effects related to the hair on the black hole will dominate the effects of dark matter.