Take the A-Metric: Interpretations of Some Known Solutions of Einstein’s Vacuum Field Equations

Charles W. Robson, Marco Ornigotti

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In this work, we present a new interpretation of the only static vacuum solution of Einstein’s field equations with planar symmetry, the Taub solution. This solution is a member of the AIII class of metrics, along with the type D Kasner solution. Various interpretations of these solutions have been put forward previously in the literature, however, some of these interpretations have suspect features and are not generally considered physical. Using a simple mathematical analysis, we show that a novel interpretation of the Taub solution is possible and that it naturally emerges from the radial, near-singularity limit of negative-mass Schwarzschild spacetime. A new, more transparent derivation is also given, showing that the type D Kasner metric can be interpreted as a region of spacetime deep within a positive-mass Schwarzschild black hole. The dual nature of this class of A-metrics is thereby demonstrated.

Original languageEnglish
Article number183
Number of pages10
Issue number3
Publication statusPublished - Mar 2022
Publication typeA1 Journal article-refereed


  • Einstein’s vacuum field equations
  • general relativity
  • Kasner solution
  • negative mass
  • Schwarzschild metric
  • Taub solution

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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