Separability of Hamilton–Jacobi and Klein–Gordon Equations in General Kerr–NUT–AdS Spacetimes

The study of the separability of the Hamilton–Jacobi and the corresponding scalar field equations in a curved spacetime has a long history. Robertson [1] and Eisenhart [2] discussed general conditions for such a separability in spaces which admit a complete set of mutually orthogonal families of hypersurfaces. An important class of 4-dimensional separable spacetimes, including several type D metrics, was found by Carter [3]. Carter also proved the separability of the Hamilton–Jacobi and the scalar field equation in the Kerr metric [4]. It was demonstrated in [5] that this separability follows from the existence of a Killing tensor. This result was generalized later, namely, it was shown that Killing and Killing–Yano tensors play an important role in the separability theory (see, e.g., [6, 7, 8, 9, 10]).