AI 中文总结
研究在金氏（2,3,0）暗物质晕中构建黑洞精确解，通过爱因斯坦场方程分析其对时空几何、光学现象、准正则模及热力学性质的影响，发现暗物质晕使黑洞有诸多变化，产生与真空不同的特征。
AI 中文摘要
近期对沉浸在天体物理暗物质环境中的黑洞解兴趣日增，我们通过完整的爱因斯坦场方程构建了由德内恩（2,3,0）暗物质晕源生的精确静态、球对称黑洞解，并研究周围晕对时空几何的物理影响。通过零测地线分析晕对光学现象的影响，表明暗物质环境显著改变光子轨迹等。通过评估不稳定零测地线的李雅普诺夫指数确定无质量准正则模行为。还计算了黑洞 - 晕系统的热力学性质。结果表明暗物质晕增大了光子球半径等，产生了与真空史瓦西情况不同的非平凡相结构。
英文摘要
Motivated by the growing recent interest in black hole solutions immersed in astrophysical dark matter environments, we construct an exact static, spherically symmetric black hole solution sourced by a King dark matter halo through the full Einstein field equations and investigate the physical consequences of the surrounding halo on the resulting spacetime geometry. The influence of the halo on optical phenomena is analyzed via null geodesics, where we show that the dark matter environment substantially modifies photon trajectories, displaces the circular photon orbits, and deforms the associated gravitational lensing structure. By evaluating the Lyapunov exponent of unstable null geodesics, we further determine the corresponding behavior of massless quasinormal modes in the eikonal regime, revealing explicit corrections to the oscillation and damping spectrum induced by the halo. We then explore the thermodynamic properties of the black hole--halo system by computing the conserved mass, Hawking temperature, entropy, heat capacity, and Gibbs free energy, allowing for a detailed assessment of both local and global thermal stability. Our analysis demonstrates that the dark matter halo increases the radius of the photon sphere and the apparent shadow, enlarges the domain of thermodynamic stability, and generates nontrivial phase structures absent in the vacuum Schwarzschild case. These results highlight that realistic dark matter environments can produce observable and thermodynamic deviations from isolated black hole geometries, potentially offering novel signatures of halo-induced gravitational effects.
