Alternative space-time for the point mass

Schwarzschild's actual exterior solution ($g_{\mathrm{S}}$) is resurrected, and together with the manifold $M_0=R^4-\{r=0\mathrm{}\}\mathrm{}$ 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 ($g_{\mathrm{DW}}$) 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 ($M_W$,$g_{\mathrm{KF}}$) 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 ($M_W$,$g_{\mathrm{KF}}$) are more in accord with what a point-mass space-time should possess than those of ($M_0$,$g_{\mathrm{S}}$). To do this, one must first explain away three seeming incongruities associated with ($M_W$,$g_{\mathrm{KF}}$): its global nonstationarity, the two-dimensional nature of its singularity, and the fact that for a finite interval of time it has no singularity at all. Finally, some of the consequences of choosing ($M_0$,$g_{\mathrm{S}}$) as the model of a point mass are discussed.