# Regularization of the Reissner-Nordstr\"om black hole

## TL;DR

This paper presents a method to regularize the Reissner-Nordström black hole by attaching an inner de Sitter region via a spherical thin-shell, removing the singularity and analyzing the stability of the resulting configuration.

## Contribution

It introduces a smooth, consistent gluing of de Sitter and Reissner-Nordström spacetimes using a thin-shell, providing a regular black hole model with stability analysis.

## Key findings

- Singularity at r=0 is removed by the de Sitter core.
- The shell's stability is governed by a modified polytropic equation of state.
- The topology becomes compact due to the inner de Sitter region.

## 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.