The separation of the Hamilton-Jacobi equation for the Kerr metric

We discuss the separability of the Hamilton-Jacobi equation for the Kerr me tric. We use a recent theorem which says that a completely integrable geode sic equation has a fully separable Hamilton-Jacobi equation if and only if the Lagrangian is a composite of the involutive first integrals. We also di scuss the physical significance of Carter's fourth constant in terms of the symplectic reduction of the Schwarzschild metric via S O(3), showing that the Killing tensor quantity is the remnant of the square of angular momentu m.