旋转黑洞对圆偏振光的散射
Scattering of circularly polarized light by a rotating black hole
摘要：
我们研究了质量为M、角动量为J的旋转（Kerr）黑洞对偏振光的散射。为了跟踪光子轨迹的偏振依赖性，可以使用以下无量纲参数：$\varepsilon=\pm (ωM)^{-1}$，其中$ω$是光子频率，符号+（-）对应于右（左）圆偏振。我们假设$|\varepsilonl << 1$，并使用[1]中发展的修正的几何光学近似，即把$\varepsilon$中的一阶偏振相关项包含在程函方程中。这些修正修改了光子的后期行为。我们证明了光子沿着零曲线运动，在极限$\varepsilon=0$成为零测地线。我们重点研究了偏振光的散射问题。即，我们考虑以下问题：（i）光子弯曲角如何依赖于它的偏振;（ii）点光源的图像的位置如何依赖于它的偏振;（iii）光子的到达时间如何依赖于它们的偏振。我们进行了数值计算，说明这些影响的一个极端旋转的黑洞，并讨论其可能的应用。
英文摘要：
We study scattering of polarized light by a rotating (Kerr) black hole of the mass M and the angular momentum J. In order to keep trace of the polarization dependence of photon trajectories one can use the following dimensionless parameter: $\varepsilon=\pm (ωM)^{-1}$, where $ω$ is the photon frequency and the sign + (-) corresponds to the right (left) circular polarization. We assume that $|\varepsilonl << 1$ and use the modified geometric optics approximation developed in [1], that is we include the first order in $\varepsilon$ polarization dependent terms into the eikonal equation. These corrections modify late time behavior of photons. We demonstrate that the photon moves along a null curve, which in the limit $\varepsilon=0$ becomes a null geodesic. We focus on the scattering problem for polarized light. Namely, we consider the following problems: (i) How does the photon bending angle depend on its polarization; (ii) How does position of the image of a point-like source depend on its polarization; (iii) How does the arrival time of photons depend on their polarization. We perform the numerical calculations that illustrate these effects for an extremely rotating black hole and discuss their possible applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
