具有物理内边缘的耗尽型德嫩暗物质晕中的黑洞及强场可观测量
Black holes in depleted Dehnen dark matter halos with physical inner edges and strong-field observables
- California State University, Fresno（弗雷斯诺州立大学）
- University of Helsinki（赫尔辛基大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构建了被耗尽德嫩暗物质晕包围的黑洞时空，推导了度规与红移解，并分析了视界、光子球、阴影等强场可观测量，揭示了晕参数的影响。
AI中文摘要：
我们构建了一个静态且球对称的黑洞时空，该时空被一个耗尽的德嫩暗物质晕所包围。该模型描述的是最终平衡态而非动力学吸积过程：初始位于指定内边缘内的晕质量被并入中心黑洞，在着装视界与存留晕之间留下一个真空间隙。因此，视界半径取决于德嫩尖点指数$\gamma$和吸收的晕质量，而当晕被移除时，施瓦西结果被精确恢复。我们推导了度规函数和红移相位的通用表达式，并为$\gamma=0,1,2,$和$5/2$获得了显式解。主能量条件施加了普适的局域界$\kappa\geq5/4$，而全局可容许性则额外依赖于尖点指数和晕的致密性。当在晕边缘施加稳定圆运动时，字面上的稳定爱因斯坦星团解释要求更强的条件$\kappa\geq3$。我们还分析了光子球、阴影和可容许参数空间，展示了晕尖点和耗尽尺度如何影响强场可观测量。先前研究的解析黑洞-晕几何以及施瓦西和弱晕极限作为一般构造的特例被包含在内。
英文摘要：
We construct a static and spherically symmetric black hole (BH) spacetime surrounded by a depleted Dehnen dark matter (DM) halo. The model describes a final equilibrium configuration rather than dynamical accretion process: the initial halo mass inside a prescribed inner edge is incorporated into the central BH, leaving a vacuum gap between the dressed horizon and the surviving halo. Consequently, the horizon radius depends on the Dehnen cusp index $γ$ and the absorbed halo mass, while the Schwarzschild result is recovered exactly when the halo is removed. We derive general expressions for the metric functions and redshift phase and obtain explicit solutions for $γ=0,1,2,$ and $5/2$. The dominant energy condition imposes the universal local bound $κ\geq5/4$, whereas global admissibility depends additionally on the cusp index and halo compactness. A literal stable Einstein-cluster interpretation requires the stronger condition $κ\geq3$ when stable circular motion is imposed at the halo edge. We also analyze the photon sphere, shadow, and admissible parameter space, demonstrating how the halo cusp and depletion scale affect strong-field observables. Previously studied analytic BH--halo geometries and the Schwarzschild and weak-halo limits follow as special cases of the general construction.
