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We study the Hamilton-Jacobi and massive Klein-Gordon equations in thegeneral Kerr-(Anti) de Sitter black hole background in all dimensions. Completeseparation of both equations is carried out in cases when there are two sets ofequal black hole rotation parameters. We analyze explicitly the symmetryproperties of these backgrounds that allow for this Liouville integrability andconstruct a nontrivial irreducible Killing tensor associated with the enlargedsymmetry group which permits separation. We also derive first-order equationsof motion for particles in these backgrounds and examine some of theirproperties. This work greatly generalizes previously known results for both theMyers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higherdimensions.Comment: 23 pages, LaTeX2

Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions