Exact solutions admitting isometry groups Gr ⫆ abelian G3

M. Ziad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Metrics admitting a minimal three dimensional Abelian isometry group, G3 are classified according to their Petrov types and metrics, giving all type O and D metrics explicitly, without imposing a source condition. The corresponding maximal Lie algebras for these metrics are obtained and identified as well. The type O metrics admit a maximal Gr (Formula Presented) G3 with r=4, 6, 7 and 10, whereas the classes of metrics of type D admit Gr (Formula Presented) G3 with r=3, 4, 5 and 6 as the maximal isometry groups. Type O metrics with a perfect fluid source are then found explicitly and are shown to admit a maximal Gr with r=4, 7 and 10. Type D perfect fluid metrics are found explicitly which admit either a maximal G3 or G4. This classification also proves that the only non-null Einstein-Maxwell field admitting a maximal G4 (Formula Presented) G3 is the type D metric (6.7) which is of Segre type [(1, 1)(11)] and is isometric to the McVittie solution.

Original languageEnglish
Article number115011
JournalJournal of Physics Communications
Issue number11
Publication statusPublished - Nov 2018


  • Einstein-Maxwell fields
  • Lie groups of dimension 3 or more
  • Metrics
  • Perfect fluids
  • Petrov types

ASJC Scopus subject areas

  • General Physics and Astronomy


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