Alternative Space-Time for the Point Mass

TL;DR

This paper revisits Schwarzschild's original solution, clarifies misconceptions about the metric attributed to Schwarzschild, and proposes an alternative space-time model for a point mass with implications for black hole interpretations.

Contribution

It demonstrates that Schwarzschild's original solution and the manifold form a consistent point-mass space-time, challenging the common interpretation of Kruskal-Fronsdal space-time.

Findings

Schwarzschild's original solution is valid as a point-mass space-time.

The metric attributed to Schwarzschild is not equivalent to Schwarzschild's original solution.

The Kruskal-Fronsdal space-time cannot be justified as a point-mass extension without modifications.

Abstract

Schwarzschild's actual exterior solution (Gs) is resurrected and together with the manifold M is shown to constitute a space-time possessing all the properties historically thought to be required of a point mass. On the other hand, the metric that today is ascribed to Schwarzschild, but which was in fact first obtained by Droste and Weyl, is shown to give rise to a space-time that is neither equivalent to Schwarzschild's nor derivable from the "historical" properties of a point mass. Consequently, the point-mass interpretation of the Kruskal-Fronsdal space-time (Mw, Gkf) can no longer be justified on the basis that it is an extension of Droste and Weyl's space-time. If such an interpretation is to be maintained, it can only be done by showing that the properties of (Mw, Gkf) are more in accord with what a point-mass space-time should possess than those of (M, Gs). To do this, one must first explain away three seeming incongruities associated with (Mw, Gkf): its global nonstationarity, the two-dimensional nature of the singularity, and the fact that for a finite interval of time it has no singularity at all. Finally, some of the consequences of choosing (M,Gs) as a model of a point-mass are discussed.