主毛发黑洞解的透镜特征
Lensing Signatures of a Primary Hair Black Hole Solution
- Dibrugarh University（迪布鲁加尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究利用引力退耦方法构造的主毛发黑洞解，在弱场和强场下计算了光线的偏转角，并基于Sgr A*阴影观测约束了主毛发参数，揭示了耦合常数对偏转的主导作用。
AI中文摘要：
我们研究了在引力退耦（GD）框架内获得的主毛发黑洞（BH）解的弱场和强场引力透镜效应。在该方法中，黑洞解是通过对已知种子时空（此处为史瓦西几何）引入几何形变而构造的。形变函数通过施加主导能量条件来确定，从而产生两个特征参数：主毛发$Q$和耦合常数$\alpha$，两者均使史瓦西时空发生形变。为了探索该黑洞的透镜性质，我们在弱场区域采用Gibbons-Werner方法，在强场区域采用Bozza形式体系。在弱场极限下，我们推导了直到二阶修正的偏转角，发现耦合参数$\alpha$对领头阶偏转的贡献比主毛发参数$Q$更显著。主毛发还表现出有效的排斥性引力行为。在强场区域，我们计算了在光子球附近传播的光子的偏转角，该偏转角呈对数发散，使得光子能够绕黑洞完成多圈并形成相对论图像。以超大质量黑洞Sgr A*作为天体物理透镜，我们进一步研究了强透镜可观测量的性质，即渐近角位置$\vartheta_{\infty}$、角间距$s$和相对星等$r_{\mathrm{mag}}$。我们还利用事件视界望远镜（EHT）合作组织报告的Sgr A*阴影观测，针对不同耦合常数$\alpha$值约束了主毛发参数$Q$。
英文摘要：
We investigate the weak and strong field gravitational lensing of light by a primary hair black hole (BH) solution obtained within the framework of the gravitational decoupling (GD) approach. In this method, the BH solution is constructed by introducing geometric deformations to a known seed spacetime, which, in the present case, is the Schwarzschild geometry. The deformation functions are determined by imposing the dominant energy condition, leading to the emergence of two characteristic parameters, the primary hair $Q$ and the coupling constant $α$, both of which deform the Schwarzschild spacetime. To explore the lensing properties of this BH, we employ the Gibbons-Werner approach in the weak field regime and Bozza's formalism in the strong field regime. In the weak field limit, we derive the deflection angle up to second-order corrections and find that the coupling parameter $α$ contributes more significantly to the leading-order deflection than the primary hair parameter $Q$. The primary hair is also found to exhibit an effectively repulsive gravitational behavior. In the strong field regime, we compute the deflection angle of photons propagating near the photon sphere, where the deflection diverges logarithmically, allowing photons to complete multiple loops around the BH and form relativistic images. Using the supermassive BH Sgr A* as the astrophysical lens, we further investigate the strong lensing observables, namely the asymptotic angular position $\vartheta_{\infty}$, the angular separation $s$, and the relative magnitude $r_{\mathrm{mag}}$. We also constrain the primary hair parameter $Q$ for different values of the coupling constant $α$ using the shadow observations of Sgr A* reported by the Event Horizon Telescope (EHT) Collaboration.
