发表机构
M.A.M.O College, University of Calicut; Providence Women’s College, University of Calicut; The Institute of Mathematical Sciences（卡利卡特大学 M.A.M.O 学院; 卡利卡特大学 Providence 女子学院; 数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究洛伦兹-欧几里得黑洞的强引力透镜，推导光子球与观测量的解析公式，发现参数$\ ho$和$k$作用相反，并利用Sgr A*和M87*阴影数据约束参数，指出可打破简并的观测量。
AI 中文摘要
我们研究了洛伦兹-欧几里得黑洞的强引力透镜性质。该时空的视界位于$r=2M$处，它并非坐标奇点，而是一个真实的度规符号改变表面，相关的曲率奇点由两个正则化参数$\ ho$和$k$消除。从零测地线方程出发，我们推导了光子球、临界碰撞参数和强偏折极限系数，并利用它们获得了偏折角以及完整的强透镜观测量集合，即相对论图像的角位置、它们的角间距、相对放大率以及连续图像之间的微分时间延迟。我们证明光子球和临界碰撞参数随$\ ho$增大而增大，随$k$增大而减小，表明这两个参数对光学几何具有相反的影响，并针对超大质量黑洞Sgr A*和M87*对所得观测量进行了数值评估。与事件视界望远镜的阴影测量比较表明，对于Sgr A*，史瓦西极限略微不受青睐，而M87*对$\ ho$施加了依赖于$k$的上限，所采用的基准值远低于这些限制。我们进一步表明，阴影仅约束$\ ho$和$k$的某种组合，并识别出能够打破这种简并的观测量，如阴影圆度、高阶图像时间延迟和准正则模谱。这些结果将引力透镜观测量确定为探测洛伦兹-欧几里得场景的有效探针。
英文摘要
We investigate the strong gravitational lensing properties of the Lorentzian Euclidean black hole, a spacetime in which the horizon at $r=2M$ is not a coordinate singularity but a genuine surface of signature change, with the associated curvature singularities removed by two regularization parameters, $ρ$ and $k$. Starting from the null geodesic equations, we derive the photon sphere, the critical impact parameter, and the strong deflection limit coefficients, and use them to obtain the deflection angle and the full set of strong lensing observables, namely the angular position of the relativistic images, their angular separation, the relative magnification, and the differential time delay between successive images. We show that the photon sphere and critical impact parameter increase with $ρ$ and decrease with $k$, indicating that the two parameters have opposite effects on the optical geometry, and evaluate the resulting observables numerically for the supermassive black holes Sgr A* and M87*. Comparison with the Event Horizon Telescope shadow measurements shows that the Schwarzschild limit is mildly disfavored for Sgr A*, whereas M87* places $k$-dependent upper bounds on $ρ$, with the adopted fiducial values lying well below these limits. We further show that the shadow constrains only a combination of $ρ$ and $k$, and identify observables such as shadow circularity, higher order image time delays, and quasinormal mode spectra that are capable of breaking this degeneracy. These results identify gravitational lensing observables as effective probes of the Lorentzian--Euclidean scenario.
Comments14 pages, 11 figures, comments are welcome
