Evolution of scalar perturbations near the Cauchy horizon of a charged black hole

Abstract

We describe the evolution of a scalar test field on the interior of a Reissner-Nordstr\"om black hole. For a wide variety of initial field configurations the energy density in the scalar field is shown to develop singularities in a neighborhood of the geometry's Cauchy horizon, suggesting that for a stellar collapse curvature singularities will develop prior to encountering the Cauchy horizon. The extension to the interior of stationary perturbations due to exterior sources is shown not to disrupt the Cauchy horizon.