Coupled gravitational and electromagnetic perturbations of Reissner-Nordstr\"om spacetime in a polarized setting II - Combined estimates for the system of wave equations

Understand

In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordstr\"om spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime.

• We analyze here the system of coupled wave equations, deriving combined energy-Morawetz and $r^p$-estimates for the system, in the case of small charge.