发表机构
Lanzhou University（兰州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对暗物质晕中的巴丁黑洞，提出一阶响应判据，揭示径向应力决定最内层稳定圆轨道位移，并验证其普适性及对极端质量比旋进相位的影响。
AI 中文摘要
仅凭暗物质密度轮廓并不能确定黑洞周围的时空；径向应力必须单独规定，并主导强场轨道响应。我们通过三个球对称模型研究赫恩奎斯特晕中的巴丁黑洞，这些模型具有相同的密度、质量函数和截断，但径向应力不同：一个具有$p_r^{\mathrm{DM}}=-ρ_{\mathrm{DM}}$的晕、其截断形式，以及一个具有$p_r^{\mathrm{DM}}=0$的截断爱因斯坦星团。将晕视为小扰动，我们推导了最内层稳定圆轨道主导位移的一阶判据，$C_λ=C_ρ+λC_p$。对于赫恩奎斯特轮廓，两个截断闭合使该轨道向相反方向移动，对五个密度轮廓的未展开计算证实了预测的符号。使用哈亚德背景和已发表的德亨晕结果的检验表明，该判据不限于巴丁-赫恩奎斯特系统。连续应力插值确定了一个临界闭合，在该闭合处主导位移消失。对于一次代表性的四年极端质量比旋进，在固定密度和截断下改变径向应力，在领先阶绝热处理中产生数弧度的相位差。
英文摘要
A dark matter density profile alone does not determine the spacetime around a black hole; the radial stress must be prescribed separately and governs the strong-field orbital response. We study a Bardeen black hole in a Hernquist halo through three spherical models sharing the same density, mass function, and cutoff but differing in radial stress: a halo with $p_r^{\mathrm{DM}}=-ρ_{\mathrm{DM}}$, its truncated form, and a truncated Einstein cluster with $p_r^{\mathrm{DM}}=0$. Treating the halo as a small perturbation, we derive a first-order criterion for the leading innermost stable circular orbit shift, $C_λ=C_ρ+λC_p$. The two truncated closures shift this orbit in opposite directions for the Hernquist profile, and unexpanded calculations for five density profiles confirm the predicted signs. Checks using a Hayward background and a published Dehnen-halo result show that the criterion is not restricted to the Bardeen-Hernquist system. A continuous stress interpolation identifies a critical closure at which the leading shift vanishes. For a representative four-year extreme-mass-ratio inspiral, changing the radial stress at fixed density and cutoff produces a phase difference of several radians in a leading-order adiabatic treatment.
Comments17 pages, 6 figures, 5 tables
