This Demonstration shows the effective potential of a black hole of given mass and charge as a function of the radius. The variable gives null paths for the value 0 and time-like paths for the value 1. If the angular momentum is zero, then by setting , the effective potential is the negative of the time component of the diagonal metric tensor.
The convention of the cosmological constant is chosen to be two times larger than conventional in most literature on the topic. The effective potential is used in the geodesic equation, which is derived from minimizing the action of the path length given some metric.