Regularization of the Reissner-Nordström black hole

Abstract

An inner de Sitter region is glued smoothly and consistently with an outer Reissner-Nordström (RN) spacetime on a spherical thin shell. Mass and charge of the outer RN spacetime are defined by the de Sitter and shell parameters. The radius of the shell plays the role of a cut-off which, by virtue of the regular de Sitter interior removes the singularity at r = 0. The topology of the inner de Sitter region with the radius of the thin shell becomes compact. For stability the perturbed shell is shown to satisfy a modified polytropic equation of state which has vanishing mass and pressure on the unperturbed shell as dictated by the junction conditions.