Photon trajectories in an asymmetric Majumdar-Papapetrou spacetime

Abstract

We study the motion of a photon that starts from the midpoint of two extremely charged stationary black holes. We investigate how the initial launching angle α and the mass of black holes determines the fate of the photon. We find that varying the mass ratio of the black holes modifies the fate of a specific photon trajectory. Furthermore, we present an exit basin diagram that depicts the final destination of a photon trajectory for a given initial condition. This basin diagram possesses a Cantor-like fractal structure that indicates chaos in the photon trajectories. Lastly, we calculate the proportion of trapped and free photons for all values of initial launching angle α with varying mass ratio. We find that the fraction of photon escapes is relatively insensitive to the mass ratio.