发表机构
Indian Institute of Technology Guwahati; Indian Institute of Astrophysics（印度理工学院古瓦哈提分校; 印度天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨暗物质晕轮廓对黑洞振铃与潮汐响应的影响，通过推导扰动方程、计算QNM谱等，提出结合振铃与潮汐响应可区分环境效应与真空黑洞几何偏差。
AI 中文摘要
天体物理黑洞（BH）并非孤立存在，而是嵌入其宿主星系提供的物质中。我们研究周围暗物质（DM）晕的形状如何修改渐近平直、静态、球对称黑洞的振铃和潮汐响应。该晕被建模为各向异性爱因斯坦星团，具有消失的径向压力和广义(α,β,γ)密度轮廓，补充了黑洞附近的内截断，以及在需要时的外潮汐截断。我们推导了轴向引力扰动方程，并使用六阶温策尔-克拉默斯-布里渊（WKB）方法和时域演化计算了准正则模式（QNM）谱。该晕会同时红移振荡频率和阻尼率，其红移量不仅由晕的紧致度决定，还由轮廓参数决定：对于中心集中的晕，内斜率γ起主导作用，而α和β则提供次要但依赖于轮廓的修正。在光锥极限下，该位移由一个单一的红移积分控制，该积分编码了光环外的晕质量分布，解释了QNM频率、光环频率和李雅普诺夫指数之间的密切对应关系。我们还表明，紧致度和轮廓形状的不同组合可产生几乎简并的振铃谱。时域演化证实了WKB频率，并显示了预期的后期Price定律衰减，其中对于缓慢衰减的轮廓，中间尾部由外密度衰减控制。最后，我们计算了静态轴向潮汐爱数，并表明它探测晕的径向权重与振铃扇区不同。因此，振铃和潮汐响应的结合提供了一种可能的方法，以区分环境效应与真空黑洞几何的真实偏差。
英文摘要
Astrophysical black holes (BH) are not isolated, but embedded in matter supplied by their host galaxies. We study how the shape of a surrounding dark matter (DM) halo modifies the ringdown and tidal response of an asymptotically flat, static, spherically symmetric BH. The halo is modelled as an anisotropic Einstein cluster with vanishing radial pressure and a generalized $(α,β,γ)$ density profile, supplemented by an inner cut-off near the BH and, where required, an outer tidal truncation. We derive the axial gravitational perturbation equation and compute the quasinormal mode (QNM) spectrum using sixth-order Wentzel-Kramers-Brillouin (WKB) methods and time-domain evolutions. The halo redshifts both the oscillation frequency and the damping rate, by an amount set not only by the halo compactness but also by the profile parameters: the inner slope $γ$ dominates for centrally concentrated halos, while $α$ and $β$ give subleading but profile-dependent corrections. In the eikonal limit, the shift is governed by a single redshift integral encoding the halo mass distribution outside the light ring, explaining the close correspondence between the QNM frequencies, the light ring frequency, and the Lyapunov exponent. We also show that different combinations of compactness and profile shape can yield nearly degenerate ringdown spectra. Time-domain evolutions confirm the WKB frequencies and display the expected late-time Price law decay, with an intermediate tail controlled by the outer density falloff for slowly decaying profiles. Finally, we compute the static axial tidal Love number and show that it probes the halo with a radial weighting different from the ringdown sector. The combined ringdown and tidal response therefore provides a possible way to distinguish environmental effects from genuine deviations of the vacuum BH geometry.
CommentsAccepted for publication in PRD
