• DOI:10.1103/PHYSREVD.20.2474
• Corpus ID: 15983002

Alternative space-time for the point mass

@article{Abrams1979AlternativeSF,
  title={Alternative space-time for the point mass},
  author={Leonard S. Abrams},
  journal={Physical Review D},
  year={1979},
  volume={20},
  pages={2474-2479}
}

• L. S. Abrams
• Published 15 November 1979
• Materials Science
• Physical Review D

Schwarzschild's actual exterior solution (${g}_{\mathrm{S}}$) is resurrected, and together with the manifold ${M}_{0}={R}^{4}\ensuremath{-}{r=0}$ 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.