Spherically symmetric static space--times which admit stationary Killing tensors of rank two

All spherically symmetric static space-times for which a nonredundant stationary Killing tensor of rank two exists are found and discussed. The results include explicit forms for the line elements, the Killing tensors, and the corresponding quadratic constants of geodesic motion. Included as special cases are relativistic analogs of the Lenz vector and of the quadratic constant of the motion peculiar to the spatial harmonic oscillator.