We rewrite expressions for a general five dimensional metric on a Kerr-(A)dS black hole background, based on the derivation given be Chen, Lü and Pope [W. Chen, H. Lu and C. N. Pope, Class. Quantum Grav. 23 (2006), 5323, hep-th/0604125]. The Klein-Gordon equation is explicitly separated using this form and we show that the angular part of the wave equation leads to just one spheroidal wave equation. We then present results for the perturbative expansion of the angular eigenvalue in powers of the rotation parameters up to 6th order and compare numerically with the continued fraction method.
Progress of Theoretical Physics 128(2), pp.227-241