偏离克尔（Kerr）：一类可分时空中的极临界曲线与光子环
Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes
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中文总结 AI 辅助
针对一类可分稳态轴对称时空，推导极临界曲线与光子环的统一解析描述，发现其仅探测临界轨道处有限局域形变值及导数，为强场几何探测提供新方法。
中文摘要 AI 辅助
黑洞临界曲线和光子环为强场几何提供互补探测手段，推动了对克尔（Kerr）之外这些可观测量的统一解析描述及其与克尔预测的直接对比。我们针对径向类的稳态轴对称可分类光测地线时空，为极观测者构建了该描述。时空依赖性通过类光动力学选定的自然光学组合，以及适合弱偏离克尔的克尔相对表示来组织。我们推导了极临界半径、李雅普诺夫指数、时间延迟和旋转参数的紧凑精确表达式，以及一旦给定特定度规的形变函数即可应用的一般一阶公式。弱偏离分析表明，极观测值的组合仅探测临界轨道处的有限组局域形变值和径向导数，而非完整径向剖面。
英文摘要
Black-hole critical curves and photon rings provide complementary probes of strong-field geometry, motivating a unified analytic description of these observables beyond Kerr and a direct comparison with the Kerr predictions. We develop such a description for polar observers in a radial class of stationary, axisymmetric spacetimes with separable null geodesics. The spacetime dependence is organized through natural optical combinations selected by the null dynamics and a Kerr-relative representation suited to weak deviations from Kerr. We derive compact exact expressions for the polar critical radius, Lyapunov exponent, time delay, and rotation parameter, together with general first-order formulas that can be applied once the deformation functions of a specific metric are supplied. The weak-deviation analysis shows that the combined polar observables probe only a finite set of local deformation values and radial derivatives at the critical orbit, rather than the full radial profiles.
发表机构
- College of Physics and Optoelectronic Engineering, Taiyuan University of Technology（太原工业大学物理与光电工程学院）
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