Geodesic Dynamics in Reissner-Nordström Geometry

Abstract

We analyze geodesics (trajectories of free-falling bodies) in the geometry created by a Reissner-Nordström black hole. Bound and unbound radial orbits are obtained first in the superextremal case, then in the extremal and subextremal cases where geodesics penetrate a horizon, inside of which an outside observer cannot see. We determine the location of geodesics in conformal (Penrose) spacetime diagrams. We also deduce that the “river model”, a useful idea to explain the behavior of Schwarzschild black holes, fails in the case where electric charge is present.