Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general nonextremal rotating charged black hole spacetimes in minimal five-dimensional gauged supergravity

We continue to investigate the separability of massive field equations for spin-0 and spin-1/2 charged particles in the general, nonextremal, rotating, charged, Chong-Cvetic-Lu-Pope black holes with two independent angular momenta and a nonzero cosmological constant in minimal D = 5 gauged super-gravity theory. We show that the complex Klein-Gordon equation and the modified Dirac equation with the inclusion of an extra counterterm can be separated by variables into purely radial and purely angular parts in this general Einstein-Maxwell-Chern-Simons background spacetime. A second-order symmetry operator that commutes with the complex Laplacian operator is constructed from the separated solutions and expressed compactly in terms of a rank-2 Stackel-Killing tensor which admits a simple diagonal form in the chosen pentad one-forms so that it can be understood as the square of a rank-3 totally antisymmetric tensor. A first-order symmetry operator that commutes with the modified Dirac operator is expressed in terms of a rank-3 generalized Killing-Yano tensor and its covariant derivative. The Hodge dual of this generalized Killing-Yano tensor is a generalized principal conformal Killing-Yano tensor of rank-2, which can generate a "tower'' of generalized (conformal) Killing-Yano and Stackel-Killing tensors that are responsible for the whole hidden symmetries of this general, rotating, charged, Kerr-anti-de Sitter black hole geometry. In addition, the first laws of black hole thermodynamics have been generalized to the case that the cosmological constant can be viewed as a thermodynamical variable.