In this report, we discuss the dynamics of photons in a five-dimensional Schwarzschild black hole. We find that the corresponding Eddington–Finkelstein-like coordinate admits two time-coordinate singularities for a particular condition. This condition is due to the existence of a non-zero angular momentum related to the extra spatial dimension. By introducing a new Regge–Wheeler tortoise coordinate, both singularities can be removed from the Eddington–Finkelstein-like coordinate. It is identified that the additional singularity is related to the photon sphere in a hyperplane, and we analyze it using a dynamical system approach. Simulation results of photon motion based on numerical calculation are presented. It is suggested that the related bending motion characteristic can probably be considered as a signature for probing the existence of the extra spatial dimension.

在本报告中，我们讨论了五维史瓦西黑洞中的光子动力学。我们发现对应的 Eddington-Finkelstein 坐标允许特定条件下的两个时间坐标奇点。这种情况是由于存在与额外空间维度相关的非零角动量。通过引入新的 Regge-Wheeler 龟坐标，可以从类 Eddington-Finkelstein 坐标中去除两个奇点。确定附加奇点与超平面中的光子球有关，我们使用动力学系统方法对其进行分析。给出了基于数值计算的光子运动模拟结果。