Screening of the Reissner–Nordström charge by a thin-shell of dust matter

A concentric charged thin-shell encircling a Reissner–Nordström black hole screens the electric/magnetic charge completely to match with an external Schwarzschild black hole. The negative mass thin-shell is shown to be stable against radial perturbations. It is shown further that by reversing the roles of inside Reissner–Nordström and outside Schwarzschild geometries the mass of the appropriate shell becomes positive.