Coupled gravitational and electromagnetic perturbations of Reissner-Nordstr\"om spacetime in a polarized setting

Understand

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordstr\"om spacetime.

• The equations are derived in the context of global non-linear stability of Reissner-Nordstr\"om under axially symmetric polarized perturbations, as a generalization of the recent work on non-linear stability of Schwarzschild spacetime of Klainerman-Szeftel.
• The main result consists in deriving, through a Chandrasekhar-type transformation, a gauge invariant quantity associated to the electromagnetic tensor that verifies a Regge-Wheeler equation.
• In this paper, we present the derivation of the main equations, postponing the estimates of the non-linear system and the construction of the dynamical spacetime to a later time.