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

Abstract

We continue to investigate the separability of massive field equations for spin-0 and spin-1/2 charged particles in the general, non-extremal, rotating, charged, Chong-Cvetic-Lu-Pope black holes with two independent angular momenta and a non-zero cosmological constant in minimal D = 5 gauged supergravity theory. We show that the complex Klein-Gordon equation and the modified Dirac equation with the inclusion of an extra counter-term 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 anti-symmetric 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-AdS 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.