Abstract
The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of the Chandrasekhar transformation introduced in the linearized setting in \cite{D-H-R-Kerr} and \cite{Ma} with the intent to use it in our ongoing project to prove the full nonlinear stability of slowly rotating Kerr as solution to the Einstein vacuum equations.
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