Angular momentum and separation constant in the Kerr metric

The Kerr metric admits a Killing tensor which yields a second-order constant of motion for classical trajectories. We find an explicit expression for this constant using a particular coordinate system, the oblate spheroidal. Owing to the separability of the Hamilton-Jacobi equation in this system, it is easy to show that the second-order constant is, in fact, the square of the total angular momentum of the particle at infinity, corrected with terms which arise from the non-inertial character of the coordinate system.