The photon trajectories around black hole with moving light source

The influence of curved spacetime around a black hole on photon trajectory has been widely studied recently. This study focuses on numerical simulations and some theoretical analysis to characterize the photons emitted from a moving light source around a Schwarzschild black hole. The results show that photon trajectories can be categorized based on the unique features of the light path caused by a variation in emitting angle (β). We propose three types of trajectories, including 1) the return angle (βret): the photon from this angle orbits around the black hole and returns to the light source 2) the escaping angle (βesc): the photon from this angle escapes to infinity parallel to the horizontal axis 3) the critical angle (βph): the photon coming from this angle of initial condition enters a critical photon orbit. The escaped photons can be subclassified by computing the lensed ratio which is the difference between the angular position of the photon escaped to infinity and the initial emitting angle. This study reveals the characteristics of photons from light source moving around a black hole and can be further used to analyze the behavior of light from compact stars or other glowing objects in more complicated systems.