Coupled gravitational and electromagnetic perturbations of Reissner–Nordström spacetime in a polarized setting

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner–Nordström spacetime. The equations are derived in the context of global nonlinear stability of Reissner–Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on non-linear stability of Schwarzschild spacetime of Klainerman–Szeftel ([9]). 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.

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Published 2 September 2020