星系中黑洞信号上的核心/尖暗物质分布印记
Imprints of core/cusp dark matter distributions on black hole signatures in galaxies
AI总结：
该研究构造了含核心/尖暗物质晕的黑洞时空，推导了强场可观测量的微扰解析表达式，分析了暗物质分布对黑洞信号的修正，为探测暗物质提供了新途径。
AI中文摘要：
在星系环境中，宿主暗物质（DM）晕可对黑洞（BH）强场可观测量施加微弱但相干的修正。我们构造了由一般核心/尖暗物质晕源产生的静态球对称黑洞时空的精确族，该暗物质晕由具有非零径向压强的各向异性应力能量张量描述。所得几何结构通过爱因斯坦方程自洽确定，适用于广泛的{α,β,γ}密度轮廓，其中包括NFW、Moore、Hernquist、Jaffe及核心/尖Dehnen模型作为特例。我们讨论了对应几何结构的渐近结构、视界位置、曲率标度和能量条件，强调内对数斜率γ控制相对论区域探测到的暗物质量。随后，我们获得了特征圆测地线的微扰解析估计，表明主导的强场修正由无量纲紧致度q_γ控制，而非仅由晕总质量决定。在q_γ的一阶近似下，我们推导了光环半径、角频率、临界碰撞参数、李雅普诺夫指数、最内稳定圆轨道（ISCO）半径及ISCO频率的解析表达式。对于尖状轮廓，光环和ISCO向外位移，而相应的轨道频率发生红移；对于核心状轮廓，此阶近似下光环半径不变，尽管其频率和捕获碰撞参数仍带有有限的环境修正。我们还研究了弱和强偏转角及其对晕内部结构的依赖关系。我们进一步讨论了这些环境修正如何影响振铃物理，特别是通过晕对准正则模式红移和后期波传播的微扰印记。
英文摘要：
In galactic environments, a host dark matter (DM) halo can imprint weak but coherent corrections on black hole (BH) strong-field observables. We construct an exact family of static and spherically symmetric BH spacetimes sourced by a generic core/cusp DM halo, described by an anisotropic stress-energy tensor with nonvanishing radial pressure. The resulting geometry is determined self-consistently from the Einstein equations for a broad $\{α,β,γ\}$ density profile, including the NFW, Moore, Hernquist, Jaffe, and core/cusp Dehnen models as special cases. We discuss the asymptotic structure, horizon location, curvature scale, and energy conditions of the corresponding geometries, emphasizing that the inner logarithmic slope $γ$ controls the amount of DM probed by the relativistic region. We then obtain perturbative analytic estimates for the characteristic circular geodesics, demonstrating that the leading strong-field corrections are controlled by the dimensionless compactness $q_γ$, rather than by the total halo mass alone. To leading order in $q_γ$, we derive analytic expressions for the light ring radius, angular frequency, critical impact parameter, Lyapunov exponent, innermost stable circular orbit (ISCO) radius, and ISCO frequency. For cuspy profiles, the light ring and ISCO are displaced outward, while the corresponding orbital frequencies are redshifted; for cored profiles, the light ring radius is unchanged at this order, although its frequency and capture impact parameter still carry finite environmental corrections. We also investigate the weak- and strong-deflection angles and their dependence on the halo's inner structure. We further discuss how these environmental corrections may affect ringdown physics, in particular through the perturbative imprint of the halo on quasinormal-mode redshifts and late-time wave propagation.
