Reinstating Schwarzschild's original manifold and its singularity

TL;DR

This paper revisits Schwarzschild's original solution, emphasizing the intrinsic and physical nature of the singularity at the Schwarzschild surface, and critiques the Kruskal extension's interpretation of the manifold.

Contribution

It reinstates Schwarzschild's original manifold, clarifies the nature of the singularity, and challenges the conventional Kruskal extension approach.

Findings

The singularity at the Schwarzschild surface is intrinsic and physical.

Hilbert's manifold's arrow of time leads to misconceptions.

An invariant quantity diverges at the Schwarzschild surface.

Abstract

The content of this review is summarized here through the titles of its sections, as follows: 1. Introduction: Schwarzschild's original solution and the ``Schwarzschild solution''. 2. The wrong arrow of time of Hilbert's manifold is at the origin of the Kruskal extension. 3. An invariant, local, intrinsic quantity that diverges at the Schwarzschild surface. 4. The singularity at the Schwarzschild surface is both intrinsic and physical. 5. Conclusion.