Specific form of the wave equation for nonextremal black holes

Klein-Gordon equation is the starting point of the scattering and gauge/gravity calculations for black holes. Thus, studying its separability and probing the residua associated with the black hole horizons are key issues that constitute the core of the calculations for the black hole internal structure. One can write the radial part of the Klein-Gordon equation in a specific form that reveals the pole structure of the horizon equation. The residua of the poles reflect the physical properties, namely surface gravities and angular velocities associated with respective horizons. We start with the Kerr black hole by showing the correspondence of the residua of the poles and the monodromy exponents. Then we study the cases of the most general nonextremal black hole solutions in four and five dimensional gauged supergravity.