Motivated by the work of Cardoso et al. (2022) [15] on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for r≪rc (rc is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for r≫rc, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass (MBH), while higher central densities (ρch) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius (rc). Smaller rc values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

中文翻译：

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Dekel-Zhao 暗物质剖面中的黑洞


受 Cardoso 等人（2022 年）[15] 对星系黑洞工作的启发，我们得出了一个被 Dekel-Zhao （DZ） 暗物质剖面包围的新黑洞解决方案。受 DZ 剖面参数影响的推导度量表现出两种不同的状态：对于 r≪rc（rc 是一个特征半径），指数校正占主导地位，在致密核心附近产生与 Schwarzschild 解的显着偏差，而对于 r≫rc，这些校正消失，在远距离恢复 Schwarzschild 度量。这些发现确保了与真空中的广义相对论的一致性。分析了黑洞阴影和偏转角，表明阴影半径随着黑洞质量 （MBH） 的增加而增加，而较高的中心密度 （ρch） 导致阴影更小，反映了致密暗物质晕对环境的影响。光子动力学揭示了 DZ 剖面如何改变临界撞击参数和有效势，其中引力透镜效应对特征半径 （rc） 高度敏感。较小的 rc 值会导致较大的偏转角，因为在致密核心附近会产生更强的引力效应。这项工作强调了暗物质剖面在塑造黑洞可观测物中的重要性，为未来的观测研究提供了理论基础，并促进了对天体物理学和宇宙学背景下暗物质-黑洞相互作用的理解。