Conformal Klein-Gordon Equations and Quasinormal Modes

Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a P\"oschl-Teller potential, here we deduce and analytically solve a conformal `radial' d'Alembert-like equation, from which we \emph{derive} QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this `radial' equation can be identified with a Schr\"odinger-like equation in which the potential is exactly the second P\"oschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.