Extended Geometry of Black Holes

TL;DR

This paper explores extending the Schwarzschild black hole solution beyond the classical singularity using new coordinate systems, revealing a stratified geometric structure that challenges traditional views of singularities.

Contribution

It introduces novel coordinate systems that allow the extension of Schwarzschild solutions beyond the singularity, resulting in a stratified geometric structure of spacetime.

Findings

Schwarzschild solution can be extended beyond r=0

The extended space-time forms an infinite covering of Kruskal space

Full four-dimensional geometry is a stratified variety

Abstract

We reconsider space-time singularities in classical Einsteinian general relativity: with the help of several new co-ordinate systems we show that the Schwarzschild solution can be extended beyond the curvature singularity at r=0. The extension appears as an infinite covering of standard Kruskal space-time. While the two-dimensional reduction of this infinite sequence of Kruskal-Szekeres domains obtained by suppressing the angular degrees of freedom is still a topological manifold - albeit one for which the metric structure is singular on one-dimensional submanifolds - we obtain for the full four-dimensional geometry the more general structure of a stratified variety.