Schwarzschild manifold and non-regular coordinate transformations (A critico-historical Note)

TL;DR

This paper critically examines the Schwarzschild manifold's metrics, emphasizing that only Schwarzschild's original and Brillouin's solutions accurately represent the physical gravity field of a point mass, unlike other extended metrics.

Contribution

It clarifies the physical validity of specific Schwarzschild solutions and critiques non-regular coordinate transformations in the context of gravitational fields.

Findings

Schwarzschild's original and Brillouin's solutions are physically adequate.

Other maximally extended metrics do not faithfully represent the gravity field.

The analysis highlights the importance of coordinate choice in gravitational solutions.

Abstract

A careful analysis of the maximally extended metrics of Schwarzschild manifold shows that the original Schwarzschild's solution (1916) and Brillouin's solution (1923) are the only ones that are adequate from the physical standpoint. Contrary to the other maximally extended metrics, they represent faithfully the gravity field created by the mass-point.