We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordstrom spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordstrom 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.

中文翻译：

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极化环境中 Reissner-Nordström 时空的耦合引力和电磁扰动

我们推导出控制 Reissner-Nordstrom 时空耦合引力和电磁扰动的方程组。这些方程是在轴对称极化扰动下 Reissner-Nordstrom 的全局非线性稳定性的背景下推导出来的，这是对 Klainerman-Szeftel 的 Schwarzschild 时空非线性稳定性最近工作的概括。主要结果包括通过 Chandrasekhar 型变换推导出与验证 Regge-Wheeler 方程的电磁张量相关的规范不变量。在本文中，我们介绍了主要方程的推导，将非线性系统的估计和动态时空的构建推迟到以后。