均匀强偏折透镜效应在近极端克尔黑洞中的应用
Uniform Strong-Deflection Lensing in Near-Extremal Kerr
- The City College of New York, City University of New York（纽约市立学院，纽约市立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构建了近极端克尔黑洞强偏折透镜从对数发散到幂律行为的均匀渐近描述，推导了交叉函数及高阶图像分支定律，并验证了其准确性。
AI中文摘要：
亚极端克尔黑洞的强偏折透镜效应表现出对数临界发散，而精确极端顺行问题则发展出更强的幂律行为。我们为顺行赤道零测地线构建了这些区域之间过渡的均匀渐近描述。当碰撞参数偏离精确临界值的量级为 \\(M\kappa\\)（其中 \\(\kappa=\sqrt{1-a^2/M^2}\\)）时，会出现显著的联合近临界与近极端极限。在此极限下，克尔径向势能简化为二次正规形式，从而产生一个解析交叉函数，连接亚极端对数区域与极端幂律区域。我们推导了匹配的次领头阶修正，并针对精确克尔测地线方程的高精度积分进行了验证，发现所有55条测试轨迹均有改进。相同的渐近结构产生了一个高阶图像分支定律，在代数累积与指数累积之间进行插值，其交叉阶数按 \\(\kappa^{-1}\\) 缩放。我们还推导并数值验证了相应的图像分支坐标时间延迟定律，其高阶极端类极限趋近于视界周期间距 \\(4\pi M\\)。
英文摘要：
Strong-deflection lensing by a subextremal Kerr black hole exhibits a logarithmic critical divergence, whereas the exactly extremal prograde problem develops stronger power-law behavior. We construct a uniform asymptotic description of the transition between these regimes for prograde equatorial null geodesics. The distinguished joint near-critical and near-extremal limit occurs when the impact-parameter offset from the exact critical value is of order \(Mκ\), where \(κ=\sqrt{1-a^2/M^2}\). In this limit, the Kerr radial potential reduces to a quadratic normal form, yielding an analytic crossover function that connects the subextremal logarithmic and extremal power-law regimes. We derive a matched next-to-leading-order correction and validate it against high-precision integrations of the exact Kerr geodesic equations, finding improvement for all 55 trajectories tested. The same asymptotic structure yields a higher-order image-branch law interpolating between algebraic and exponential accumulation, with crossover order scaling as \(κ^{-1}\). We also derive and numerically validate the corresponding image-branch coordinate-time delay law, whose high-order extremal-like limit approaches the horizon-period spacing \(4πM\).
