Angular momentum and separation constant in the Kerr metric

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Abstract
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.