AI 中文总结
该研究分析PFDM、常数ω暗物质、BEC暗物质三种模型对静态球对称黑洞时空几何的影响，计算强引力可观测量并结合EHT约束，证实强引力可观测量可用于区分暗物质模型。
AI 中文摘要
我们研究三种符合物理动机的暗物质物态方程如何改变广义相对论中静态球对称黑洞的时空几何。所考虑的模型包括各向异性完美流体暗物质（PFDM）、各向同性常数ω暗物质，以及具有多方物态方程（EoS）的玻色-爱因斯坦凝聚（BEC）暗物质。对于每个模型，我们推导爱因斯坦场方程，并在PFDM和常数ω情形下解析求解度规函数，对于BEC暗物质则通过托尔曼-奥本海默-沃尔科夫（TOV）方程数值求解。随后我们计算关键的强引力可观测量：事件视界半径、光子球半径、黑洞阴影半径、最内稳定圆轨道（ISCO）以及圆轨道速度分布。将各模型得到的阴影半径与事件视界望远镜的约束进行比较，以对暗物质参数施加界限。通过零能量条件、弱能量条件、主导能量条件和强能量条件，以及声速的因果性要求来评估物理可行性。我们的结果表明，PFDM产生接近史瓦西的几何，带有轻微的各向异性修正；常数ω模型受因果性严格限制为0≤ω≤1；BEC暗物质产生由玻色子自相互作用参数K控制的平滑、有界偏差。综合来看，这些发现表明，强引力可观测量可作为实用工具，通过暗物质模型在黑洞时空中留下的几何印记来区分相互竞争的暗物质模型。
英文摘要
We study how three physically motivated dark matter equations of state alter the spacetime geometry of static, spherically symmetric black holes in General Relativity. The models considered are anisotropic perfect fluid dark matter (PFDM), isotropic constant-$ω$ dark matter, and Bose-Einstein condensate (BEC) dark matter with a polytropic equation of state (EoS). For each model, we derive the Einstein field equations and solve for the metric function analytically in the PFDM and constant-$ω$ cases, and numerically via the Tolman-Oppenheimer-Volkoff equations for BEC dark matter. We then compute the key strong gravity observables: event horizon radius, photon sphere radius, black hole shadow radius, innermost stable circular orbit (ISCO), and circular orbital velocity profiles. The shadow radii obtained for each model are compared against the Event Horizon Telescope constraints to place bounds on the dark matter parameters. Physical viability is assessed through the null, weak, dominant, and strong energy conditions, along with causality requirements on the sound speed. Our results show that PFDM produces near Schwarzschild geometry with mild anisotropic corrections, the constant-$ω$ model is strongly restricted by causality to $0 \leq ω\leq 1$, and BEC dark matter generates smooth, bounded deviations governed by the bosonic self-interaction parameter K. Taken together, these findings show that strong gravity observables can serve as practical tools for distinguishing between competing dark matter models through their geometric imprints on black hole space times.
