AI 中文总结
该研究利用引力解耦框架构建带毛黑洞，分析其视界结构、光学特征与标量准正则模式，发现固定视界半径无法唯一确定时空性质，多类观测可互补探测这类黑洞几何。
AI 中文摘要
引力解耦为从已知（种子）解（如史瓦西解）构建黑洞几何提供了系统框架，其外部性质与种子解极为相似，同时仍保留着潜在可区分的特征。利用该方法，我们研究了一类静态、球对称的带毛黑洞，考察这类形变如何影响其视界结构、光子球、阴影尺度以及标量准正则模式（QNM）。我们首先通过施加相关的视界和能量条件要求，确定参数空间的物理可控区域，仅保留这些区域之外的构型用于探索性对比。为分离几何效应，我们在相同视界半径下对比解，同时明确考虑种子几何中的质量参数与渐近测得的ADM质量之间的区别。所得的ADM归一化阴影尺度被用于与M87*和Sgr A*的特征角尺度进行示例对比。我们还采用六阶温策尔-克拉默斯-布里渊（Wentzel-Kramers-Brillouin）近似与改进的渐近迭代方法计算无质量标量QNM，发现所考虑的模式间吻合度较高。我们的结果表明，固定视界半径并不能唯一确定时空的光学或微扰性质，而质量归一化会显著改变对几何趋势的解读。因此，视界结构、零测地线可观测量与标量QNM为探测引力解耦黑洞几何提供了互补的探针。
英文摘要
Gravitational-decoupling provides a systematic framework for constructing black hole geometries from known (seed) solutions (such as the Schwarzschild), whose exterior properties closely resemble those of the seed solution while still retaining potentially distinguishable features. Using this approach, we study a class of static, spherically symmetric hairy black holes and examine how such deformations affect their horizon structure, photon spheres, shadow scales, and scalar quasinormal modes (QNMs). We first determine the physically controlled regions of the parameter space by imposing the relevant horizon and energy condition requirements, while retaining configurations outside these domains only for exploratory comparison. To isolate geometric effects, we compare solutions at a common horizon radius, while accounting explicitly for the distinction between the mass parameter entering the seed geometry and the ADM mass measured asymptotically. The resulting ADM normalized shadow scales are used for an illustrative comparison with the characteristic angular scales of M87* and Sgr A*. We also compute massless scalar QNMs using the sixth-order Wentzel-Kramers-Brillouin approximation and the improved Asymptotic Iteration Method, finding close agreement over the modes considered. Our results show that fixing the horizon radius does not uniquely determine either the optical or perturbative properties of the spacetime, and that mass normalization can significantly alter the interpretation of geometric trends. Horizon structure, null geodesic observables, and scalar QNMs therefore provide complementary probes of gravitationally-decoupled black hole geometries.
Comments36 pages, 3 figures
