Kerr时空等离子体中的光传播：Hamilton-Jacobi方程的分离和阴影的计算
Light propagation in a plasma on Kerr spacetime: Separation of the Hamilton-Jacobi equation and calculation of the shadow
摘要：
本文研究光在克尔黑洞周围非磁化无压等离子体中的传播。我们找到了等离子体电子密度必须满足的充要条件，以保证光线的Hamilton-Jacobi方程是可分的，即，广义卡特常数存在对于满足该条件的所有情况，我们确定光子区域，即，时空中存在球形光线的区域。球形光线是停留在球体$r = \mathrm{constant}$上的光线（在Boyer-Lindquist坐标中）。基于这些结果，我们计算了在满足分离条件的等离子体影响下的克尔黑洞的阴影。更准确地说，我们推导出一个解析公式的阴影的天空中的观察者，位于任何地方的域的外部通信的边界曲线。给出了几个算例。
英文摘要：
We consider light propagation in a non-magnetized pressureless plasma around a Kerr black hole. We find the necessary and sufficient condition the plasma electron density has to satisfy to guarantee that the Hamilton-Jacobi equation for the light rays is separable, i.e., that a generalized Carter constant exists. For all cases where this condition is satisfied we determine the photon region, i.e., the region in the spacetime where spherical light rays exist. A spherical light ray is a light ray that stays on a sphere $r = \mathrm{constant}$ (in Boyer-Lindquist coordinates). Based on these results, we calculate the shadow of a Kerr black hole under the influence of a plasma that satisfies the separability condition. More precisely, we derive an analytical formula for the boundary curve of the shadow on the sky of an observer that is located anywhere in the domain of outer communication. Several examples are worked out.
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