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The analytic proof of mode stability of the Kerr black hole was provided byWhiting. In his proof, the construction of a conserved quantity for unstablemode was crucial. We extend the method of the analysis for the Kerr-de Sittergeometry. The perturbation equations of massless fields in the Kerr-de Sittergeometry can be transformed into Heun's equations which have four regularsingularities. In this paper we investigate differential and integraltransformations of solutions of the equations. Using those we construct aconserved quantity for unstable modes in the Kerr-de Sitter geometry, anddiscuss its property.Comment: 13 pages, LaTe

A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry