Boundedness and decay for the Teukolsky system of spin \(\pm 2\) on Reissner-Nordström spacetime: the case \(|Q| \ll M\) (Q2195861)

This paper studies two generalizations of the Teukolsky equations of black hole perturbations for the case of charged black holes. The first one is an equation for the extreme component of the curvature. The second is an equation for a gauge invariant quantity involving the electromagnetic curvature components. Boundedness and decay statements are proved. The proof is based on \textit{M. Dafermos} et al. [Acta Math. 222, No. 1, 1--214 (2019; Zbl 1419.83023)]. These provide the first steps in proving the full linear stability of the Reissner-Nordström metric for gravitational and electromagnetic perturbations.