On the Stability of a Wormhole in the Maximally-Extended Reissner-Nordstr\"om Solution

TL;DR

This paper investigates the stability of the inner horizon in the maximally extended Reissner-Nordström black hole solution, demonstrating that collapse prevents observers from reaching white hole or parallel universe regions, thus preserving cosmic censorship.

Contribution

It shows that the collapse of the inner horizon due to perturbations ensures observers cannot access non-physical regions, reinforcing the stability of the black hole's causal structure.

Findings

Inner horizon collapse prevents access to white hole regions

Observers inevitably hit the central singularity when passing through the inner horizon

Collapse of the inner horizon supports cosmic censorship hypothesis

Abstract

We consider the stability of the maximally-extended Reissner-Nordstr\"om solution in a Minkowski, de Sitter, or anti-de Sitter background. In a broad class of situations, prior work has shown that spherically symmetric perturbations from a massless scalar field cause the inner horizon of an RN black hole to become singular and collapse. Even if this is the case, it may still be possible for an observer to travel through the inner horizon before it fully collapses, thus violating strong cosmic censorship. In this work, we show that the collapse of the inner horizon and the occurrence of a singularity along the inner horizon are sufficient to prevent an observer from accessing the white hole regions and the parallel universe regions of the maximally extended RN space-time. Thus, if an observer passes through the inner horizon, they will inevitably hit the central singularity. Throughout this article, we use natural units where c = G = 4 {\pi} {\epsilon}_0 = 1.