Global Kruskal-Szekeres coordinates for Reissner-Nordstr\"om spacetime

TL;DR

This paper introduces a new global coordinate system for the Reissner-Nordström spacetime that simplifies its diagrammatic representation and offers clearer physical insights into its structure.

Contribution

It derives a smooth, global Kruskal-Szekeres coordinate chart for the maximal extension of non-extremal Reissner-Nordström spacetime, generalizing standard coordinates.

Findings

Provides a global coordinate chart for Reissner-Nordström spacetime.

Simplifies the spacetime's conformal diagram.

Offers a transparent physical interpretation of the spacetime structure.

Abstract

I derive a smooth and global Kruskal-Szekeres coordinate chart for the maximal extension of the non-extremal Reissner-Nordstr\"om geometry that provides a generalization to the standard inner and outer Kruskal-Szekeres coordinates. The Kruskal-Szekeres diagram associated to this coordinate chart, whose existence is an interesting fact in and on itself, provides a simple alternative with a transparent physical interpretation to the conformal diagram of the spacetime.