Type: Article
Publication Date: 2019-01-08
Citations: 62
DOI: https://doi.org/10.1007/s40818-018-0058-8
We prove boundedness and polynomial decay statements for solutions of the spin ±2 Teukolsky equation on a Kerr exterior background with parameters satisfying |a|≪M . The bounds are obtained by introducing generalisations of the higher order quantities P and P_ used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters |a|<M . As in the Schwarzschild case, these bounds provide the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.