Regularization of the Reissner-Nordstr\"om black hole

Abstract

An inner de Sitter region is glued smoothly and consistently with an outer Reissner-Nordstr\"{o}m (RN) spacetime on a spherical thin-shell. Mass and charge of the outer RN spacetime are defined by the de Sitter and shell parameters. Radius of the shell plays the role of a cut-off which by virtue of regular de Sitter inside removes the singularity at $r=0.$ The topology of inner de Sitter 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.