Potential Functions Admitted by Well-Known Spherically Symmetric Static Spacetimes

Conformal groups, which also represent the point symmetries of wave and Klein-Gordon equations, give rise to interesting forms of an associated potential function. The exact nature of the relationship between the conformal groups and the wave and Klein-Gordon equations is given by a geometric condition, that we exploit to determine a variety of potentials functions. Due to the volume of potentials, we display the results in tables.