The linear stability of Reissner-Nordstr\"om spacetime for small charge

Understand

In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordstr\"om family of charged black holes with small charge.

• Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordstr\"om solution arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to a linearized Kerr-Newman metric.
• We express the perturbations in geodesic outgoing null foliations, also known as Bondi gauge.
• To obtain decay of the solution, one must add a residual pure gauge solution which is proved to be itself controlled from initial data.