Characterizing planetary orbits and trajectories of light in the Reissner-Nordstrom metric

Abstract

Exact analytic expressions for planetary orbits and light trajectories in the Reissner-Nordstrom geometry are presented. They are characterized in a map specified by three dimensionless parameters for the planetary orbits, while two dimensionless parameters are required to map the trajectories of light. Notable differences with the corresponding orbits and trajectories in the Schwarzschild geometry are indicated. In particular, when the energy and angular momentum of the planet are fixed, the precession angle of the orbit decreases as the net electric charge of the massive star or black hole increases. A similar result also holds for the deflection angle of a light ray.