On Schwarzschild anti De Sitter and Reissner N\"ordstrom Wormholes

TL;DR

This paper analyzes wormholes related to Schwarzschild, Schwarzschild anti De Sitter, and Reissner-Nordstrom black holes across different coordinate systems, demonstrating their non-traversability due to bridge pinching-off.

Contribution

It provides an explicit proof of the non-traversability of these wormholes using Kruskal-Szekeres coordinates and discusses the case of extreme Reissner-Nordstrom black holes.

Findings

Wormholes are non-traversable due to bridge pinching-off.

Embedding exists only for finite radial intervals in certain coordinates.

Kruskal-Szekeres coordinates reveal the non-traversability explicitly.

Abstract

We discuss the wormholes associated with the four-dimensional Schwarzschild (S4), Schwarzschild anti De Sitter (SaDS4), and Reissner-N\"ordstrom (RN4) black holes, in Schwarzschild, isotropic and Kruskal-Szekeres cordinates. The first two coordinate systems are valid outside the horizons, while the third one is used for the interiors. In Schwarzschild coordinates, embedding for SaDS4 exists only for a finite interval of the radial coordinate r, and similar restrictions exist for RN4. The use of the K-S coordinates allows us to give an explicit proof of the pinching-off of the bridges, making them non-traversable. The case of the extreme Reissner-N\"ordstrom (ERN4) is also discussed.